Methods and systems for performing digital assays using polydisperse droplets

ABSTRACT

Methods, devices, and systems for performing digital assays are provided. In certain aspects, the methods, devices, and systems can be used for the amplification and detection of nucleic acids. In certain aspects, the methods, devices, and systems can be used for the recognition, detection, and sizing of droplets in a volume. Also provided are compositions and kits suitable for use with the methods and devices of the present disclosure.

CROSS-REFERENCE

This application is a continuation of U.S. application Ser. No.15/301,798, filed Oct. 4, 2016, which is a national stage entry ofInternational Application No. PCT/US2015/024840, filed Apr. 8, 2015,which claims the benefit of U.S. Provisional Application No. 61/976,918,filed Apr. 8, 2014, and U.S. Provisional Application No. 62/047,570,filed Sep. 8, 2014, all of which are incorporated herein by reference intheir entirety.

STATEMENT AS TO FEDERALLY SPONSORED RESEARCH

This invention was made with government support under R21 GM103459,awarded by the National Institutes of Health. The government has certainrights in the invention.

BACKGROUND OF THE INVENTION

Digital assays, in which measurements are made based on a counting ofbinary yes or no responses, are increasingly important in biology, owingto their robustness, sensitivity and accuracy. Whereas analogmeasurements often require calibration with a running standard, digitalmeasurements do not require calibration, and have the potential to befaster, easier to implement, more accurate, and more robust than analogmethods.

An important application for digital assays is accurate detection andmeasurement of DNA or RNA in a sample. The most commonly used method todetect DNA in a sample is polymerase chain reaction (PCR), wherein DNAis amplified in a temperature-sensitive reaction catalyzed by aDNA-polymerizing enzyme. In PCR the sample is typically cycled betweentwo or three temperatures ranging from about 60° C. to about 95° C. by athermal cycling device. The use of PCR to amplify DNA has greatlyadvanced a wide range of disciplines, from basic biology to clinicaldiagnostics and forensics. One particular form of PCR that is often usedin diagnostics and biomedical research is quantitative PCR (qPCR), whichnot only detects the presence of DNA in the sample, but also provides anaccurate measure of its concentration.

The most commonly used method for conducting qPCR is real-time PCR,wherein the absolute concentration of a sample is inferred from the timeevolution of the amplification process, which is monitored repeatedlyduring the thermal cycling process with a fluorescent probe, such as amolecular beacon or Taqman probe, that specifically recognizes theamplification product.

Real-time PCR is susceptible to various errors, including the formationof unwanted primer dimers, where primer molecules attach to each otherbecause of complementary stretches in their sequence. As a result, aby-product is generated that competes with the target element foravailable PCR reagents, thus potentially inhibiting amplification of thetarget sequence and interfering with accurate quantification. Thequantification of target also requires precise knowledge of theamplification efficiency for each cycle, and because the growth isexponential, tiny uncertainties in amplification efficiency (e.g., belowthe threshold detection level) will result in very large errors in thedetermination of target copy numbers. This error can become very largewhen the initial concentration of nucleic acid is low or when thefluorescence detection is not sufficiently sensitive. Thus, despite itspower to identify and quantify target DNA from complex samples,real-time PCR is not able to reliably and precisely quantify low sampleconcentrations, as required for example in the detection of pathogens orclinical diagnostics.

The limits of real-time PCR to quantify low copy-number DNA accuratelycan potentially be overcome using digital PCR (dPCR). In dPCR, a volumecontaining a sample is divided into an array of smaller volumes, suchthat, based on Poisson statistics, at least some of the volumes do notcontain target DNA, while the rest can contain one or more targetmolecules. DNA amplification is then carried out in an array of thesmaller volumes simultaneously, resulting in an increase in fluorescence(or other signal) in only those volumes that contained one or moretarget molecules prior to amplification. The DNA copy number can beeasily and accurately determined by knowing the volumes and the numberof wells with an increased signal (i.e., those that contain amplifiedDNA) compared to the total number of wells.

Most existing digital assays rely on a count of binary responsesobtained from volumes of invariant size, such as monodisperse dropletemulsions. While advances in microfluidic systems have enabled thegeneration of monodisperse droplet emulsions, these systems aretechnically difficult, resulting in increased time and cost for theend-user when compared with conventional analog methods.

Given the limitations inherent in analog assays such as real-time PCR,and the technical difficulties of existing digital assays, it is clearthat there is a need to provide improved methods and apparatuses forperforming digital assays. The invention described herein addresses thisneed and more.

SUMMARY OF THE INVENTION

The present disclosure provides methods, systems, compositions and kitsfor performing digital assays. The present disclosure relates in part tothe surprising discovery digital assays can be performed in systemscontaining polydisperse droplets without the introduction of undueexperimental error.

In various aspects, the present methods, systems, compositions and kitscan be used to perform digital PCR assays involving the amplification ofa nucleotide sample.

In various aspects, the present disclosure provides methods forperforming a digital assay, comprising: producing a plurality ofpolydisperse droplets, wherein at least some of the droplets comprise asample; amplifying the sample; labeling the sample with a detectableagent; obtaining an image stack for a droplet; determining from theimage stack the volume of the droplet; determining from the image stackthe presence or absence of the detectable agent in the droplet; anddetermining the concentration of the sample in the plurality of dropletsbased on the presence or absence of the detectable agent in a pluralityof droplets.

In some aspects, the present disclosure provides methods for performinga digital assay, comprising: producing a plurality of polydispersedroplets, wherein at least some of the droplets comprise a sample;amplifying the sample; labeling the sample with a detectable agent;flowing the plurality of polydisperse droplets through a flow cytometrychannel; determining the volume of a droplet as it flows through theflow cytometry channel; determining the presence or absence of thedetectable agent in the droplet; and determining the concentration ofthe sample in the plurality of droplets based on the presence or absenceof the detectable agent in a plurality of droplets.

In various aspects, the present disclosure provides compositions andkits for performing a digital assay comprising: a first fluid; a secondfluid, wherein the first fluid and the second fluid are immiscible ineach other and are capable of forming an emulsion when physicallyagitated; a surfactant; and an amplification reagent.

In various aspects, the present disclosure provides methods,compositions and kits for performing digital assays using doubleemulsions. In some aspects, the double emulsion comprises two aqueousphases and an oil phase.

In various aspects, the present disclosure provides methods forperforming a digital assay. A plurality of polydisperse droplets may beproduced. At least some of the droplets may comprise a sample. Thesample may be amplified. The sample may be labeled with a detectableagent. An image stack for a droplet may be obtained. The volume of thedroplet may be determined from the image stack. The presence or absenceof the detectable agent in the droplet may be determined from the imagestack. The concentration of the sample in the plurality of droplets maybe determined based on the presence or absence of the detectable agentin the plurality of droplets.

In various aspects, the present disclosure provides methods forperforming a digital assay. A plurality of polydisperse droplets may beproduced. At least some of the droplets may comprise a sample. Thesample may be amplified. The sample may be labeled with a detectableagent. The plurality of polydisperse droplets may be flowed through aflow cytometry channel. The volume of a droplet may be determined as itflows through the flow cytometry channel. The presence or absence of thedetectable agent in the droplet may be determined. The concentration ofthe sample in the plurality of droplets may be determined based on thepresence or absence of the detectable agent in the plurality ofpolydisperse droplets. In some aspects, the size of the droplet may bedetermined by detecting light scattered from the droplet. Theconcentration of the sample in the plurality of polydisperse dropletsmay be determined based on the sizes or size distribution of thedroplets.

In various aspects, the present disclosure provides compositions forperforming digital assays. A composition may comprise a first fluid, asecond fluid, a surfactant, and an amplification reagent. The firstfluid and the second fluid may be immiscible in each other and may becapable of forming an emulsion when agitated. In some aspects, thecomposition may further comprise a sample, such as a nucleotide, and/ora detectable agent capable of labeling the sample.

In various aspects, the present disclosure provides systems fordetermining a volume of at least one droplet. The system may comprise acontainer, an imaging source, and a computing device. The container maybe configured for holding the droplet(s). The imaging source may beconfigured to obtain an image of the droplet(s) in the container. Thecomputing device may comprise a processor and a memory (e.g., anon-transitory, tangible computer-readable storage medium such as a ROM,RAM, flash memory, or the like). The memory may store a set ofinstructions that when executed by the processor cause (i) the imagingsource to obtain an image stack of the droplet(s) and (ii) the processorto determine the volume of the droplet(s) in the sample based on theobtained image stack.

In various aspects, the present disclosure provides methods fordetermining a volume of a droplet. An image stack of the droplet may beobtained. A pixel set(s) in an individual image of the image stack maybe identified. The pixel set(s) may be identified as corresponding to atleast a part of at least one droplet. An individual droplet(s) may beidentified from the pixel set(s) based on the correspondence. The volumeof the identified individual droplet(s) may be determined based on theat least one pixel set. The part of at least one droplet may comprise apart of a single droplet, parts of multiple droplets, a whole droplet, aplurality of whole droplets, or combinations thereof.

In various aspects, the present disclosure provides systems forperforming digital assays. The system may comprise a container, animaging source, and a computing device. The container may be configuredfor holding a plurality of polydisperse droplets. At least some of thedroplets may comprise a sample labeled with a detectable agent. Theimaging source may be configured to obtain an image stack of theplurality of polydisperse droplets held in the container. The computingdevice may be configured to operate the imaging source. The computingdevice may comprise a processor and a memory (e.g., a non-transitory,tangible computer-readable storage medium such as a ROM, RAM, flashmemory, or the like). The memory may store a set of instructions thatwhen executed by the processor cause (i) the imaging source to obtainthe image stack of the plurality of polydisperse droplets held in thecontainer, (ii) the processor to determine the volumes of the pluralityof polydisperse droplets based on the obtained image stack, (iii) theprocessor to determine the presence or absence of the detectable agentin the plurality of polydisperse droplets, and (iv) the processor todetermine the concentration of the sample in the plurality of dropletsbased on the presence or absence of the detectable agent in theplurality of polydisperse droplets and the volumes of the plurality ofpolydisperse droplets.

BRIEF DESCRIPTION OF THE DRAWINGS

The novel features of the disclosure are set forth with particularity inthe appended claims. A better understanding of the features andadvantages of the present disclosure will be obtained by reference tothe following detailed description that sets forth illustrativeembodiments, in which the principles of the disclosure are utilized, andthe accompanying drawings of which:

FIG. 1 is a gray-scale image of an exemplary polydisperse dropletemulsion system obtained using confocal fluorescent microscopy.

FIG. 2A schematically illustrates an exemplary detection systemconfigured to analyze the presence or absence of sample in a pluralityof droplets.

FIG. 2B schematically illustrates an exemplary detection method toanalyze the presence and or absence of sample in a plurality ofdroplets.

FIG. 2C schematically illustrates another exemplary detection method toanalyze the presence and or absence of sample in a plurality ofdroplets.

FIG. 2D schematically illustrates an exemplary scan detection method toidentify droplets in a volume, which may be used with the system of FIG.2A to implement the methods of FIGS. 2B and 2A.

FIG. 2E schematically illustrates an exemplary Simple Boundary Method toidentify droplets in a volume, which may be used with the system of FIG.2A to implement the methods of FIGS. 2B and 2A.

FIG. 2F schematically illustrates an exemplary Reverse Watershed Methodto identify droplets in a volume, which may be used with the system ofFIG. 2A to implement the methods of FIGS. 2B and 2A.

FIG. 2G schematically illustrates an exemplary Circle Detection Methodto identify droplets in a volume, which may be used with the system ofFIG. 2A to implement the methods of FIGS. 2B and 2A.

FIG. 2H schematically illustrates an exemplary combined reversewatershed and Circle Detection Method to identify droplets in a volume,which may be used with the system of FIG. 2A to implement the methods ofFIGS. 2B and 2A.

FIG. 3 depicts an exemplary method for performing a digital assayaccording to one aspect of the present disclosure. According to thisaspect, polydisperse droplets containing a nucleotide sample can beproduced by vortexing (Step 3A), the nucleotides can be amplified by PCR(Step 3B), and the nucleotide sample can be analyzed in a multi-wellplate format (Step 3C).

FIG. 4 depicts an exemplary method for performing a digital assayaccording to one aspect of the present disclosure. According to thisaspect, emulsion PCR can be performed as part of an optimizedhigh-throughput system with minimal need for sample transfer. Accordingto this aspect, oil and aqueous PCR components are loaded onto amulti-well plate, the entire multi-well plate is vortexed to induceemulsification, the nucleotide components undergo PCR amplification in athermal cycler, and the resulting products are imaged with afluorescence microscope.

FIGS. 5A and 5B depict the results of the initial steps of the ReverseWatershed Method as applied to the image in FIG. 1, including theidentification of regions of interest (ROIs) as shown in FIG. 5A and thefinal, processed image with optimized circular regions as shown in FIG.5B, from which information on droplet size and target molecule presencecan be determined.

FIG. 6A shows a processed image produced after performing the initialsteps of the Circle Detection Method as applied to the image of FIG. 1.FIG. 6B shows the final results obtained after sorting circles in FIG.6A to identify and locate droplets.

FIG. 7A shows a processed image produced after performing the initialsteps of the combined reverse watershed and Circle Detection Method asapplied to the image of FIG. 1. FIG. 7B shoes the final results obtainedafter sorting circles in FIG. 7A to identify and locate droplets.

FIGS. 8A and 8B show fluorescence images of a polydisperse dropletemulsion acquired with a scanning confocal microscope for redfluorescence (FIG. 8A) and green fluorescence (FIG. 8B) detectionsystems. Circles in FIGS. 8A and 8B indicate identified droplets. Graphson the right of FIGS. 8A and 8B depict fluorescence intensities alongthe straight lines depicted in the images on the left. FIG. 8C shows thedistribution of droplet diameters of 489 droplets measured afteremulsification using the ROX fluorescence signal.

FIG. 9 shows the frequency distributions of the ratio of green-to-redfluorescence intensities for populations of polydisperse droplets loadedwith three different starting concentrations of dsDNA (˜2×10³ dsDNAcopies/4 in Histogram 9A, ˜2×10⁶ dsDNA copies/4 in Histogram 9B, and˜2×10⁷ dsDNA copies/4 in FIG. Histogram 9C).

FIG. 10 shows a computer-generated clipped log normal distribution ofdroplet diameters used in computer simulations to validate methods forperforming digital assays. The distribution is an idealizedapproximation of the experimental distribution shown in FIG. 8C.

FIG. 11 shows the relationship between sample size (i.e., number ofdroplets, shown on the horizontal axis), errors in droplet diametermeasurements, and errors in the measurement of a sample concentration(measurement variability, shown on the vertical axis). Data weregenerated using computer simulations of a digital assay performed withthe sample concentration set to 4.4×10⁻⁵ molecules/fL.

FIG. 12 shows the relationship between sample concentration and thestatistical power with which a sample of a given concentration can bedistinguished using a digital assay from a second sample having aconcentration that is 50% higher.

FIG. 13 shows the relationship between sample size (number of droplets,shown on the horizontal axis) and dynamic range (shown on the verticalaxis) of a digital assay when performed on polydisperse droplets (graycircles) or monodisperse droplets (black triangles) with no dropletdiameter measurement error.

FIG. 14 shows the frequency of droplet fusion events that occur eitherspontaneously, or as a result of thermal cycling, in polydispersedroplet emulsions. Emulsified droplets containing ROX but no greenfluorescent probe were combined with droplets containing greenfluorescent probe but no ROX. The combined mixture, shown in Image 14A(red fluorescence) and Image 14B (green fluorescence), was then eitherleft at room temperature to serve as a control (no heating) or wassubjected to a hot start and one of 1 or 50 thermal cycles. Thefrequency of droplet fusion events is reflected in the percent ofdroplets containing both ROX and green fluorescent probe (Chart 14C).

FIG. 15 shows the frequency of polydisperse droplet diameters subjectedto no heating (white bars), 1 (gray bars) or 50 thermal cycles (blackbars).

FIG. 16 shows the improvements in data acquisition capabilities achievedwith refractive index matching of the fluids making up a polydispersedroplet emulsion. Fluorescence images were acquired at progressivelydeeper (from left to right) focal planes from two different emulsionsystems (depicted in FIG. 16, A1-A5 and FIG. 16, B1-B5, respectively)with a confocal microscope. In the aqueous sample (FIG. 16, A1-A5), therefractive indices of the two immiscible fluid components are disparate,and the droplet boundaries become progressively less clear in imagesacquired at deeper planes of focus, as in FIG. 16, A5. In the mixedwater and glycerol sample (FIG. 16, B1-B5), the refractive indices ofthe two immiscible fluid components are similar, and the dropletboundaries remain clear even in images acquired at deeper planes offocus, as in FIG. 16, B5.

FIG. 17 shows fluorescence images of a water/oil/water double emulsion.

FIG. 18. shows the relationship between sample concentration values asdetermined by a best-fit method (shown on the vertical axis) and asdetermined by absorption measurements at 260 nm (shown on horizontalaxis) for samples loaded with concentrations of dsDNA spanning fourorders of magnitude (2×10³, 2×10⁴, 2×10⁵ and 2×10⁶ dsDNA copies/4 ofpurified dsDNA).

DETAILED DESCRIPTION

The present disclosure relates to methods and systems for performingdigital assays using polydisperse droplets. In particular, the presentdisclosure relates to methods for the amplification and analysis ofsamples in polydisperse droplet systems. The present methods and systemscan be used to identify droplets in a polydisperse droplet system,determine whether that droplet contains a sample of interest, and theperformance of assay steps, such as for example, digital polymerasechain reaction (dPCR).

The methods and systems of the present disclosure advantageously enablethe performance of high-throughput amplification and analysis of samplesthrough the use of polydisperse droplets. The present disclosureexhibits significantly improved dynamic ranges in the performance of adigital assay by generating volumes of variable size. For a given sampleconcentration, the size of the volumes can define the probability ofbeing occupied by one or more molecules (e.g., template molecules) ofinterest. In the example of amplification-related techniques, variationof volume size can be used to alter this occupational probability andthus the number of wells or sample volumes (e.g., droplets) that showamplification. Notably, the present disclosure improves upon existingtechniques that simply increase the number of volumes with constant sizeso as to increase the dynamic range. Unlike the existing methods, theuse of variable-volume samples eliminates the need to use a large areato accommodate the volumes needed to expand dynamic range, which, e.g.,increases the likelihood of defects on a chip where some digitizedvolumes do not form properly or have other defects. In addition,increasing the number of volumes also increases the time required toanalyze all those digitized volumes.

The present disclosure provides devices, systems and apparatuses thatcan be used in the generation, manipulation, analysis, and modeling ofpolydisperse droplet samples. Related methods are also provided. Thedisclosure also includes a method for the analysis of digitalquantification platforms. While designed to enable digital assays usingpolydisperse platforms, the disclosure can also be applied to thedigital assays using monodisperse emulsion platforms. The disclosurealso includes methods for emulsion distribution modeling, dataacquisition and emulsion generation.

Some aspects of the present disclosure include methods and apparatusesfor the manipulation and analysis of species that comprise, but are notlimited to, chemicals, biochemicals, genetic materials (e.g., DNA, RNA,and the like), expressed products of genetic materials, proteins,metabolites, peptides, polypeptides, crystallizing molecules, orbiological cells including rare cells, cellular fractions, organelles,exosomes, mitochondria, drugs, biological particles that circulate inperipheral blood or lymphatic systems, or particles.

In some aspects, the apparatus, devices, methods and systems of thepresent disclosure can be used to amplify a polynucleotide sample, suchas with polymerase chain reaction (PCR), reverse transcriptase PCR(RT-PCR), ligase chain reaction (LCR), loop mediated amplification(LAMP), reverse transcription loop mediated amplification (RT-LAMP),helicase dependent amplification (HDA), reverse transcription helicasedependent amplification (RT-HDA), recombinase polymerase amplification(RPA), reverse transcription recombinase polymerase amplification(RT-RPA), catalytic hairpin assembly reactions (CHA), hybridizationchain reaction (HCR), entropy-driven catalysis, strand displacementamplification (SDA), and/or reverse transcription strand displacementamplification (RT-SDA). In certain aspects, the apparatus, devices,methods and systems of the present disclosure can be used for nucleicacid sequence based amplification (NASBA), transcription mediatedamplification (TMA), self-sustained sequence replication (3SR), andsingle primer isothermal amplification (SPIA). Other techniques that canbe used include, e.g., signal mediated amplification of RNA technology(SMART), rolling circle amplification (RCA), hyper branched rollingcircle amplification (HRCA), exponential amplification reaction (EXPAR),smart amplification (SmartAmp), isothermal and chimeric primer-initiatedamplification of nucleic acids (ICANS), and multiple displacementamplification (MDA). Other aspects can include the crystallization ofproteins and small molecules, the manipulation and/or analysis of cells(e.g., rare cells or single cells), the manipulation and/or analysis ofother biological particles (e.g., isolated mitochondria, bacteria, viralparticles), or other biological or chemical components.

Polydisperse Droplet Emulsions for Digital Assays

The present disclosure provides methods, systems, and devices forperforming digital assays with increased dynamic range, where a largenumber of volumes of varying size is generated. Unlike existingplatforms, the methods and systems of the present disclosure can includeuse of a distribution of sizes (e.g., volumes) that is continuous ratherthan discrete. In some aspects, droplets of variable size can be createdin various ways, either randomly or through controlled application ofmicrofluidics. For example, microfluidic generation of constant volumedroplets is well known in the art by using a T-junction or flow-focusingdevice. In these systems, the size of the droplet can be controlled bythe shear rate and channel dimensions. If for a given T-junctiongeometry the shear rate is continuously varied, droplets of differentvolumes can be generated. These methods can be realized, e.g., bycomputer-controlled syringe pumps or modulated air pressure, whichadjusts the relative flow speeds of the aqueous phase and the oilcarrier fluid.

In various aspects of the present disclosure, an emulsion ofpolydisperse droplets can be produced between two or more immisciblefluids. As used herein, the term “immiscible fluids” means two or morefluids that, under a given set of experimental conditions, do notundergo mixing or blending to an appreciable degree to form ahomogeneous mixture, even when in physical contact with one another.

As described further herein, the volumes used for digital measurementscan be generated and analyzed by a variety of ways. The presentdisclosure includes a sample holder that can be used to hold the volumesso that the volumes can be further processed and/or analyzed. The sampleholders of the present disclosure can include test tubes,microcentrifuge tubes, arrays of wells in a standard multi-well plate,arrays of wells on a microarray or in a microfluidic chip, amicrofluidic chip configured to generate droplets, as well as othercommercially available or otherwise generally known devices capable ofholding discrete volumes (e.g., wells or droplets) of a sample.

In some aspects, droplets of various sizes can be generated randomly, byemulsification in a sample holder (e.g., a test tube). Dropletrandomness can simplify the experiment because, e.g., no effort need bemade to control the size of droplets. During emulsification, droplets ofdifferent volume can be stabilized with the use of any suitablesurfactants. The emulsification approach is particularly useful forseveral reasons: (1) the method is compatible with basic instrumentationfound in every biomedical laboratory, (2) droplet generation is simple;it does not require complex chip design or sophisticated equipment forflow control, (3) the droplets are not confined in individual wells,which minimizes the space required to accommodate a large number ofdroplets and (4) the assay is simple because the same container can beused for droplet generation and droplet storage during amplification.Advantageously, using this method, no sample transfer is needed betweendroplet generation and the amplification reaction.

Some aspects of the present disclosure include producing droplets inimmiscible fluids. As is well known in the art, a wide variety ofimmiscible fluids can be combined to produce droplets of varyingvolumes. As described further herein, the fluids can be combined througha variety of ways, such as by emulsification. For example, an aqueoussolution (e.g., water) can be combined with a non-aqueous fluid (e.g.,oil) to produce droplets in a sample holder or on a microfluidic chip.Aqueous solutions suitable for use in the present disclosure can includea water-based solution that can further include buffers, salts, andother components generally known to be used in detection assays, such asPCR. Thus, aqueous solutions described herein can include, e.g.,primers, nucleotides, and probes. Suitable non-aqueous fluids caninclude, but are not limited to, an organic phase fluid such as amineral oil (e.g., light mineral oil), a silicone oil, a fluorinated oilor fluid (e.g., a fluorinated alcohol or Fluorinert), other commerciallyavailable materials (e.g., Tegosoft), or a combination thereof.

Emulsions can be generated in a variety of ways. According to certainaspects of the present disclosure, an emulsion can be generated byagitation, which is typically physical agitation. Some methods ofphysical agitation for emulsion generation include, but are not limitedto, shaking, vortexing (that can include vortexing individual tubes orentire well plates or other devices), sonicating, mixing with magnets,rapid pipetting or some other extrusion method, or via flow focusingwithin microfluidic devices, among other methods. The agitation usedaccording to the present disclosure can be any suitable agitation meansthat is sufficient to give rise to an emulsion. For example, the speed,degree, and time used for vortexing, sonicating, pipetting, extrusion orother agitation methods can readily be adjusted such that it issufficient to give rise to an emulsion system of the present disclosure.The particular characteristics of the emulsion can be tuned by adjustingthe chemical components in the system and the agitation conditions thatthe system is subjected to.

A variety of fluids or liquids can be used to prepare an emulsionaccording to the present disclosure. In some aspects, the systemincludes two or more immiscible fluids, that when mixed underappropriate conditions, separate into a dispersed droplet phase and acontinuous carrier phase. For example a first fluid, which will becomethe dispersed droplet phase, can contain a sample. In some aspects, thisfirst fluid will be an aqueous solution. In some aspects, this firstfluid will remain a liquid, in other aspects, it can be, or become, agel or a solid. In some aspects, this first fluid can have or can form adistinct shell.

Possible aqueous fluids that can be used as one phase of a dropletemulsion include, but are not limited to, various PCR and RT-PCRsolutions, isothermal amplification solutions such as for LAMP or NASBA,blood samples, plasma samples, serum samples, solutions that containcell lysates or secretions or bacterial lysates or secretions, and otherbiological samples containing proteins, bacteria, viral particles and/orcells (eukaryotic, prokaryotic, or particles thereof) among others. Incertain aspects, the aqueous fluids can also contain surfactants orother agents to facilitate desired interactions and/or compatibilitywith immiscible fluids and/or other materials or interfaces they maycome in contact with. In certain aspects, the aqueous solutions loadedon the devices can have cells expressing a malignant phenotype, fetalcells, circulating endothelial cells, tumor cells, cells infected with avirus, cells transfected with a gene of interest, or T-cells or B-cellspresent in the peripheral blood of subjects afflicted with autoimmune orautoreactive disorders, or other subtypes of immune cells, or rare cellsor biological particles (e.g., exosomes, mitochondria) that circulate inperipheral blood or in the lymphatic system or spinal fluids or otherbody fluids. The cells or biological particles can, in somecircumstances, be rare in a sample and the discretization can be used,for example, to spatially isolate the cells, thereby allowing fordetection of the rare cells or biological particles.

In some aspects, the second fluid, which would become the continuousphase, will be a fluid that is immiscible with the first fluid. Thesecond fluid is sometimes referred to as an oil, but does not need to bean oil. Potential fluids that can serve as the second fluid include butare not limited to, fluorocarbon based oils, silicon compound basedoils, hydrocarbon based oils such as mineral oil and hexadecane,vegetable based oils, ionic liquids, an aqueous phase immiscible withthe first aqueous phase, or that forms a physical barrier with the firstphase, supercritical fluids, air or other gas phases.

In certain aspects of the present disclosure, the polydisperse dropletscan comprise a fluid interface modification. Fluid interfacemodification elements include interface stabilizing or modifyingmolecules such as, but not limited to, surfactants, lipids,phospholipids, glycolipids, proteins, peptides, nanoparticles, polymers,precipitants, microparticles, a molecule with a hydrophobic portion anda hydrophilic portion, or other components. In some aspects, one or morefluid interface modification elements can be present in a fluid thatwill be comprised in a disperse droplet phase fluid. In other aspects,one or more fluid interface modification elements can be present in afluid that will be comprised in a continuous carrier phase fluid. Instill other aspects one or more fluid interface modification elementscan be present in both disperse droplet phase fluids and continuouscarrier phase fluids. The fluid interface modification elements presentin a fluid that will be comprised in one phase of the emulsion can bethe same or different from the fluid interface modification elementspresent in a fluid that will be comprised in another phase of theemulsion.

In some aspects, of the present disclosure, the fluid interfacemodification element can be used to prevent coalescence of neighboringemulsion droplets, leading to long-term emulsion stability. In someaspects, fluid interface modification elements can have some other oradditional important role, such as providing a biocompatible surfacewithin droplets, which may or may not also contribute to emulsionstability. In some aspects, the components can play a role incontrolling transport of components between the fluids or betweendroplets. Some non-limiting examples of fluid interface modificationelements include without limitation ABIL WE 09, ABIL EM90, TEGOSOFT DEC,bovine serum albumin (BSA), sorbitans (e.g., Span 80), polysorbates(e.g., PEG-ylated sorbitan such as TWEEN 20 and TWEEN 80), sodiumdodecylsulfate (SDS), 1H,1H,2H,2H-perfluorooctanol (PFO), Triton-X 100,monolein, oleic acid, phospholipids, and Pico-Surf, as well as variousfluorinated surfactants, among others.

In some aspects, the emulsion system will consist of a dispersed aqueousphase, containing the sample of interest, surrounded by a continuous oilphase. Other aspects can be variations or modifications of this system,or they can be emulsions of completely different composition orconstruction. Alternative emulsion systems include multiple emulsionssuch as water in oil in water (water/oil/water, or w/o/w) emulsions, oroil in water in oil (oil/water/oil, or o/w/o) emulsions. These multipleemulsion systems would then have inner, middle and outer phases. In someaspects, the inner and outer phases can have the same composition. Inother aspects, the inner and outer phases can be similar—for example,both aqueous, or both the same oil—but with different sub-components. Inother aspects, all three emulsion phases can have different, andsometimes very different, compositions.

In certain aspects, the emulsion system can comprise two immisciblefluids that are both aqueous or both non-aqueous. In further aspects,both emulsion fluids can be oil based where the oils are immiscible witheach other. For example, one of the oils can be a hydrocarbon-based oiland the other oil can be a fluorocarbon based oil. In other emulsionsystems, both fluids can be primarily aqueous but still be immisciblewith each other. In some aspects, this occurs when the aqueous solutionscontain components that phase separate from each other. Some examples ofsolutes that can be used include, but are not limited to, systemscontaining dextran, ficoll, methylcellulose, polyethylene glycol (PEG)of varying length, copolymers of polyethylene glycol and polypropyleneglycol, polyvinyl alcohol (PVA), polyvinyl pyrrolidone (PVP), ReppalPES, K₃PO₄, sodium citrate, sodium sulfate, Na₂HPO₄, and K₃PO₄.

In addition to aqueous solutions and non-aqueous fluids, surfactants canalso be included to, e.g., improve stability of the droplets and/or tofacilitate droplet formation. Suitable surfactants can include, but arenot limited to, non-ionic surfactants, ionic surfactants, silicone-basedsurfactants, fluorinated surfactants or a combination thereof. Non-ionicsurfactants can include, for example, sorbitan monostearate (Span 60),octylphenoxyethoxyethanol (Triton X-100), polyoxyethylenesorbitanmonooleate (Tween 80) and sorbitan monooleate (Span 80). Silicone-basedsurfactants can include, for example, ABIL WE 09 surfactant. Other typesof surfactants generally well known in the art can similarly be used. Insome aspects, the surfactant can be present at a variety ofconcentrations or ranges of concentrations, such as approximately 0.01%,0.1%, 0.25%, 0.5%, 1%, 5%, or 10% by weight.

In certain aspects, the polydisperse droplets of the present disclosurehave a continuous volume distribution. As provided herein, the term“continuous volume distribution” is intended to describe a distributionof volumes that vary continuously, rather than by pre-defined discretesteps, across the volume distribution. For example, chip-based platformscan include well or droplet volumes that cover a volume distributiondefined by pre-defined, discrete steps fabricated as part of the chip.That is, a chip can be made to have volumes present at 100 nL, 10 nL,and 1 nL, with no other volumes present in between those discrete steps.In contrast, a continuous volume distribution in not pre-defined (i.e.,the volume distribution is undefined prior to producing or formingdroplet volumes). The continuous volume distributions can, for example,be produced via emulsification, as described further herein. Inemulsions, the volumes (e.g., droplet volumes) have a discrete volumebut the droplet volumes in the distribution are undefined prior toproducing the droplets (i.e., not pre-defined by fabrication techniques)and the volumes are randomly distributed along the continuous volumedistribution. According to the present disclosure, an emulsificationsystem can be produced by physical agitation, such as for examplevortexing or shaking the sample. An upper and lower boundary for dropletvolumes can be modified by the forces imparted on the emulsion (e.g., bythe speed of vortexing or the intensity of shaking). However, thedroplet volumes generated by such techniques continuously vary along thevolume distribution produced.

According to various aspects of the present disclosure, polydispersedroplets are formed through emulsification of two or more immisciblefluids. According to these aspects, at least some of the polydispersedroplets contain the sample, which is subsequently amplified andanalyzed by the presently described methods. As used herein, the term“polydisperse” refers to plurality of droplets in a droplet systemhaving a continuous volume distribution. The minimum, maximum, mean, andmedian droplet diameters, and their respective standard deviations, fora given polydisperse droplet system depend on the physical properties ofthe emulsion (e.g., chemical components and temperature) and the mannerin which the polydisperse droplet were formed (e.g., the type andduration of the physical agitation that gave rise to the polydispersedroplet system). The distribution of droplets and their respectiveprobabilities can be tuned by adjusting these parameters for a givensystem.

In some aspects, continuous volume distributions can also becharacterized such that for any set (or plurality) of droplet volumes,its distribution function can be denoted f(x), where f(x)dx is theprobability that a given droplet in the set will have a volume between xand x+dx. (dx is an infinitesimally small number.) In certain aspects, acontinuous distribution is one where the volumes of the droplets in thedroplet set are (1) not pre-specified and (2) that for some rangex_lower<x<x_upper, f(x) is always greater than zero (x_lower cannot beequal to x_upper, and nothing more needs to be known about f(x)). Thus,the present disclosure can in some aspects, include using a droplet setdrawn from a continuous distribution, measuring the volume of eachdroplet in the set and using the measured droplet volumes in analysis.

FIG. 8C shows an experimentally measured distribution of dropletdiameters and their respective probabilities generated according to thepresently described methods and systems. The distribution ofexperimentally determined droplet diameters and probabilities areconsistent with theoretically determined values, as depicted in FIG. 10,and both figures depict a continuous volume distribution for droplets.

As described herein, the volumes can be produced having a variety ofvolume distributions, which can be analyzed using a variety of differentmethods. In some aspects, a sample can contain a molecule or moleculesof interest that can be analyzed. Discrete volumes of the sample can begenerated for analysis via digital measurements. For example, themethods herein can include producing a plurality of droplets having avolume distribution. In some aspects, the plurality of droplets of thesample can be produced in an emulsion that includes combining immisciblefluids, as further described herein. In one example, a sample caninclude an aqueous solution that includes a molecule of interest (e.g.,a nucleic acid molecule). The sample can be mixed with an oil to formdroplets of the sample suspended in the oil. Depending on the methodused, the volumes of the plurality of droplets in the emulsion can berandomly distributed along a continuous volume distribution.Furthermore, the ranges of volumes can be controlled by the method usedto form the emulsions. For example, intensity of vortexing, shaking,sonicating, and/or extrusion can be controlled to produce a desiredvolume distribution, or by varying the composition of the surfactantand/or oil.

As will be appreciated by one of ordinary skill in the art, the rangesfor and volumes within a volume distribution will depend on a variety offactors for a given analysis. In some aspects, the volume distributionsof the plurality of droplets can include a volume range from about 100nanoliters (nL) to about 1 femtoliter (fL), from about 10 nL to about 10fL, from about 1 nL to about 100 fL, from about 100 nL to about 1picoliter (pL), from about 10 nL to about 10 pL, from about 1 nL toabout 1 pL, from about 500 pL to about 50 fL, from about 100 pL to about100 fL. Depending on the selected factors for producing droplets, it isroutine to define the upper and lower boundaries of a volumedistribution by, e.g., changing the intensity of mixing a sample and oilwith a surfactant. There can be ranges of volumes in the volumedistributions. For example, volumes in the distributions can range bymore than a factor of 2, by more than a factor of 10, by more than afactor of 100, by more than a factor of 1000, by more than a factor of10000, by more than a factor of 100000, by more than a factor of1000000, by more than a factor of about 2, by more than a factor ofabout 10, by more than a factor of about 100, by more than a factor ofabout 1000, by more than a factor of about 10000, by more than a factorof about 100000 or by more than a factor of 1000000. By ranging by afactor of 2, the lower boundary of the volume distribution can be, e.g.,10 nL with an upper boundary of 20 nL. Similarly, by ranging by a factor10, the lower boundary of the volume distribution can be, e.g., 10 nLwith an upper boundary of 100 nL.

In some aspects, of the present disclosure, the polydisperse dropletshave a distribution of droplet diameters with a standard deviationgreater than 1000%, greater than 500%, greater than 100%, greater than50%, greater than 30%, greater than 20%, greater than 15%, greater than10%, greater than 9%, greater than 8%, greater than 7%, greater than 6%,or greater than 5% of the median droplet diameter.

In some aspects, of the present disclosure, the polydisperse dropletshave a distribution of droplet diameters with a standard deviationgreater than 1000%, greater than 500%, greater than 100%, greater than50%, greater than 30%, greater than 20%, greater than 15%, greater than10%, greater than 9%, greater than 8%, greater than 7%, greater than 6%,or greater than 5% of the mean droplet diameter.

In some aspects, of the present disclosure, the volumes can be createdusing valves, wells, or droplets. Here, droplets of different volumes(diameters) can be generated using a wide range of methods. In onemethod, droplets of a defined volume are generated using microfluidics(e.g., with T-channel or flow focusing as well known in the art); byvarying the shear rate or channel dimension, droplets of different sizescan be formed. In another method, the droplets of different volumes aregenerated by emulsification with the aid of different surfactants; herethe droplets of different volumes are stabilized and are controlled withthe use of different surfactants. With either method, amplification ofanalyte (e.g., digital PCR) can be carried out simultaneously in alldroplets of different volumes (sizes). In certain aspects, the dropletscan then be flowed in a single-file format through a flow cytometer orother similar device where the size of the droplet can be determined andthe fluorescence from the droplet can be interrogated. When using flowcytometry or other flow-through methods, the presence of amplificationproduct in each droplet is determined based on fluorescence and the size(volume) of each droplet is determined based on the scattering signalfrom the droplet. Alternatively, the size can be determined by taking animage as the droplet passes through the apparatus in a manner similar toimage-based flow cytometry. In this way, by noting both the size of eachdroplet and the presence or absence of amplification product in eachdroplet of a given size, it is possible to back-calculate the originalconcentration of the analyte present in the sample after interrogating asufficient number of droplets of different sizes. Because the dropletsare of different sizes, for a given dynamic range, the analysis is muchfaster than if the droplets are all of a similar size for reasonsdiscussed previously.

In certain aspects, the present methods and systems can be used toanalyze samples in digitized volumes. The term “digitized volumes”refers to the volumes produced after obtaining an initial sample andseparating it into physically distinct smaller volumes in preparationfor an assay.

According to certain aspects of the present disclosure, droplets can beformed and assayed in a chip. According to further aspects,amplification and digital measurements can take place in a digitizationchip.

In one aspect, the present disclosure provides a method for creatingconcentration gradients that are integrated with digital measurement andreadout. For example, one can integrate microfluidic gradient generationwith a sample digitization chip. For increasing the dynamic range, alogarithmic or exponential concentration gradient is preferred, but anumber of methods are now available for forming various types and shapesof concentration gradients on chip, including nonlinear gradients suchas power, exponential, error, Gaussian, and cubic root functions.

According to certain aspects of the present disclosure, a concentrationgradient in a microfluidic device can be used in which there are onlytwo inlet reservoirs or channels, but more would also be suitable foruse of the disclosure. According to this aspect, one inlet is used forthe sample and one for buffer (or PCR reagent in the case of digitalPCR). As the two solutions flow through the network, the sample solutionbecomes diluted by the buffer (water or PCR reagent) solution in apre-defined fashion such that at each of the outlet channels, adifferent concentration of the sample is present. Linear, polynomial,and logarithmic gradients spanning six orders of magnitude have all beengenerated using variations of this design.

In another aspect, a logarithmic or exponential gradient spanning sixorders of magnitude in concentration is used. The sample and PCRsolution is pipetted into the two inlet reservoirs, after which theywill pass over the array of wells. Once the wells have been filled withthe concentration gradient, light mineral oil or some other immisciblefluid is flowed over the wells to create individual digitized volumeswithin the wells. The wells in this example are of the same volume. Inanother aspect of the disclosure, wells of varying volumes can be used.

In another aspect, the sample and PCR solution is pipetted into the twoinlet reservoirs, after which they will pass over an array ofhydrophilic and hydrophobic patches. As the sample flows over thehydrophilic patches, they cause the formation of wetted droplets ofdifferent size sample volumes. Alternatively, the sample can bedigitized.

In another aspect of the disclosure, the gradients are used inconjunction with digitized volumes created using valves, wells, ordroplets. In the aspect with droplets, the droplets can be formed in acontinuous-flow fashion either in the T-channel geometry or in the flowfocusing geometry, both of which are well known in the art.

To digitize the sample that had been diluted, a digitization scheme canbe used. Here, the sample solution containing different concentrationsof target molecule are flown over the topographically patterned surfaceto form digitized and discrete volumes for subsequent digitalmeasurements and readout. Alternatively, it is possible to digitize thesample using a patterned surface.

In another aspect, the sample can be digitized using microfluidicchannels and immiscible fluid phases. In this aspect, the sample phaseis introduced into the channel, followed by an immiscible phase whichforms discrete sample volumes that are defined by the geometricdimensions of the side cavities (D. E. Cohen, T. Schneider, M. Wang, D.T. Chiu, Anal. Chem. 82, 5707-5717).

According to one exemplary aspect, the present disclosure providesarrays of digitized volumes of different sizes, where patterned surfacesare used to create arrays of volumes of different sizes. According tothis aspect, seven sets of arrays are created, where each array contains900 digitized volumes (30×30). The array is formed by creatinghydrophilic circular patches in a background of a hydrophobic surface.As a result, when the surface is exposed to aqueous solution and oil,the hydrophilic patches will be covered by an aqueous drop surrounded byoil. The droplet can be hemi-spherical, but the shape can change (eithermore pancaked or more rounded) depending on the exact surfaces we useand the oil and aqueous solution used. In one aspect, a heavy oil isused, and the drop is more pancaked because the oil will push on thedrop.

The circles that define each set of the 900 hydrophilic patches havedifferent sizes, ranging from 1 μm in diameter to 5 μm to 10 μm to 50 μmto 100 μm to 500 μm and finally to 1 mm in diameter. Because the volumeof the drop scales roughly as cubic to the diameter of the drop,increasing the diameter of the patch by ten times increases the volumeby about 1,000 times. As a result, using digitized volumes of varyingsizes is more efficient in terms of space and readout than simply usingmore digitized volumes of the same size. In one aspect, 900 digitizedvolumes for each set of the array is used because this number issuitable for arriving at a statistically robust digital readout.However, depending on the particular application and the neededrobustness of the readout, either more digitized volumes within each setof array or less digitized volumes can be designed. According to thisaspect, a large array of digitized volumes can be produced with varyingsizes due to the ease of surface patterning hydrophilic patches ofdifferent sizes. This aspect can be useful for applications such asdigital PCR where a wide dynamic range is often desired, it is highlybeneficial to perform PCR in drops that are created using patternedsurfaces.

In certain aspects, a dispersed droplet system can undergo a change froma liquid to a solid phase for at least a portion of the disperseddroplet system. In some aspects, liquids of the disperse droplet systemcan be converted to a solid through a gelation process. For example, asolution of agarose can solidify as the temperature falls below itsmelting temperature. In further aspects, a liquid-to-solid conversioncan occur through the formation of calcium alginate from solubleprecursors, by photopolymerization of solution components, the use ofcross-linking agents that induce polymerization. In some aspects, entiredroplets are solidified solidify, while in other aspects, only a layerat the interface solidifies.

In some aspects, emulsion systems of the present disclosure can beconfigured such that the degree of diffusion between the droplet and thesurrounding media can be enhanced or minimized, depending upon theapplication of interest. In certain aspects, the polydisperse dropletemulsion system can be designed to enhance diffusion of reagents betweenthe droplet and the surrounding phase. In certain aspects, thepolydisperse droplet emulsion system can be designed to reduce oreliminate diffusion of reagents between the droplet and the surroundingphase. For example, agarose droplets formed at temperatures above theagarose melting temperature solidify when cooled to room temperatureand, depending on the concentration of agarose in the solution,diffusion within or across the drop boundary can occur. In certainaspects, the composition of the droplet and surrounding media can betuned to maximize diffusion after droplet encapsulation. The propertiesof droplets can also be tuned to prevent unwanted diffusion, e.g., of atarget molecule. In certain aspects, target molecules can becross-linked or anchored in place. For example, key molecules such asprimers can be anchored to the matrix. Anchoring target molecules inplace can enable the use of emulsions in non-oil based platforms, whichcan have the advantage of better facilitating downstream processing orsample recovery, among other advantages.

In some aspects, a physical barrier can be created between the phases ina disperse droplet system. In certain aspects, a physical barriersurrounding the droplet can be a polymerized solid shell, a lipidbilayer, a precipitated interface, or an aggregation of a material suchas proteins, nanoparticles, vesicles, precipitants, microscopicparticles or other materials at the interface.

Other modifications to the emulsion system can be made to alter certainproperties that can benefit the manipulation, processing or analysis ofthe emulsion. Depending on the method of analysis, different physicaland optical properties of the emulsion system can play a very importantrole. These include, but are not limited to, the size distribution ofthe emulsion droplets, the relative density of the fluids, the viscosityof the fluids, the refractive index of the fluids and the overall andlocal density of the droplets within the continuous fluid.

Refractive index matching can be beneficial for improving the imagingdepth for optical analysis (e.g., reducing distortions of dropletboundaries). The refractive index of the aqueous phase is typicallyclose to the refractive index of waters, i.e., approximately n=1.33. Therefractive index of the aqueous phase is typically lower than that ofhydrocarbon-based oils, but slightly higher than that of fluorinatedoils. In one aspect of the present disclosure, refractive index matchingcan be achieved by adding high refractive index (i.e., n>1.45)components such as, but not limited to, glycerol, sucrose, Cargilleoptical liquids, ethylene glycol, propylene glycol, CS2, methylsalicylate, dimethyl sulfoxide (DMSO), among others to the aqueous phaseof the emulsion to enable the refractive index of an aqueous phase tomore closely match that of the oil. In other aspects, refractive indexmatching can be achieved by adjusting the refractive index of thenon-aqueous phase typically consisting of a mixture of a component witha higher refractive index and a component with a lower refractive indexthan the aqueous phase. Any suitable additive can be used to raise therefractive index of a low-refractive index fluid, such as, but notlimited to fluorocarbon-based oils (e.g., perfluorodecalin; Fluorinertoils such as e.g., FC-40, FC-70; Krytox oils, among others, with highrefractive index (i.e., n=1.36-1.4); fluorocarbon solvents, such as butnot limited to octafluorotoluene, hexafluorobenzene, petafluorobenzene,1,2,4,5-tetrafluorobenzene decafluoro-p-xylol, among others. Table 1below provides a non-inclusive list of additives that can be used toadjust the refractive index of the non-aqueous phase, thereby causing itto more closely match that of the aqueous phase (i.e., water, n=1.33):

TABLE 1 Summary of physical properties of a selection of fluorocarbonoils and solvents listed in order of ascending refractive index. Wateris included for reference. Refractive Density Boiling Point ChemicalName Index, n (g/cm³) (° C.) Fluorinert FC-40 oil 1.29 1.855 165Fluorinert FC-70 oil 1.303 1.94 215 Perfluorodecalin 1.3145 1.908 142Water 1.333 1.00 100 decafluoro-p-xylol 1.3606 1.651 121-122octafluorotoluene 1.368 1.666 104 hexafluorobenzene 1.377 1.612 80-82pentafluorobenzene 1.391 1.514  85 1,2,4,5-tetrafluorobenzene 1.4071.344  90 1,3,5-trifluorobenzene 1.414 1.277 75-76 1,4-difluorobenzene1.441 1.11 88-89 fluorobenzene 1.465 1.024  85 1-ethynyl-4-fluorobenzene1.516 1.048 55-56

Proper spacing of droplets is important to maximize the number ofdroplets that can be analyzed without information from one dropletinterfering with another droplet. In some aspects, the space betweendroplets can be increased by altering the density of the oil system. Forexample, partly fluorinated hydrocarbon compounds can be used to lowerthe density of a fluorocarbon oil. In another aspect the density of anaqueous solution can be altered by adding CSCl or some other suitabledensity increasing component. For example a solution containing CSCl at56% by weight would have a density near 1.7 g/mL, and at 65% would havea density of approximately 1.9 g/mL, with these closely matching thedensity of many fluorocarbons. The viscosity of the oil can also bealtered so that the droplets move more slowly and/or to increase thewetting layer between droplets. In another aspect, the second fluid canexperience a phase transition to a more solid nature so that thediscrete phase is trapped at certain positions. In another aspect doubleemulsions (e.g., w/o/w) can be used to pack droplets close togetherwhile also preventing direct contact/overlap.

In some aspects, the distribution of droplet diameters has a standarddeviation greater than 1000%, greater than 500%, greater than 100%,greater than 50%, greater than 30%, greater than 20%, greater than 15%,greater than 10%, greater than 9%, greater than 8%, greater than 7%,greater than 6%, or greater than 5% of the median droplet diameter. Insome aspects, the distribution of droplet diameters has a standarddeviation greater than about 1000%, greater than about 500%, greaterthan about 100%, greater than about 50%, greater than about 30%, greaterthan about 20%, greater than about 15%, greater than about 10%, greaterthan about 9%, greater than about 8%, greater than about 7%, greaterthan about 6%, or greater than about 5% of the median droplet diameter.

In other aspects, the distribution of droplet diameters has a standarddeviation greater than 1000%, greater than 500%, greater than 100%,greater than 50%, greater than 30%, greater than 20%, greater than 15%,greater than 10%, greater than 9%, greater than 8%, greater than 7%,greater than 6%, or greater than 5% of the mean droplet diameter. Insome aspects, the distribution of droplet diameters has a standarddeviation greater than about 1000%, greater than about 500%, greaterthan about 100%, greater than about 50%, greater than about 30%, greaterthan about 20%, greater than about 15%, greater than about 10%, greaterthan about 9%, greater than about 8%, greater than about 7%, greaterthan about 6%, or greater than about 5% of the mean droplet diameter.

In further aspects, the volumes in the polydisperse droplets vary bymore than a factor of 2, by more than a factor of 10, by more than afactor of 100, by more than a factor of 1000, by more than a factor of10000, by more than a factor of 100000, by more than a factor of1000000, by more than a factor of 2, by more than a factor of 10, bymore than a factor of 100. In yet further aspects, the volumes in thepolydisperse droplets vary by more than a factor of about 2, more than afactor of about 10, or by more than a factor of about 100, by more thana factor of about 1000, by more than a factor of about 10000, by morethan a factor of about 100000 or by more than a factor of 1000000.

In some aspects, the polydisperse droplets have a volume distribution offrom 100 nanoliters (nL) to 1 femtoliters (fL), from 10 nL to 10 fL,from 1 nL to 100 fL, from 100 nL to 1 pL, from 10 nL to 10 pL, or from 1nL to 1 pL, from 500 pL to 50 fL, from 100 pL to 100 fL. In furtheraspects, the polydisperse droplets have a volume distribution of fromabout 100 nanoliters (nL) to about 1 femtoliters (fL), from about 10 nLto about 10 fL, from about 1 nL to about 100 fL, from about 100 nL toabout 1 pL, from about 10 nL to about 10 pL, or from about 1 nL to about1 pL, from about 500 pL to about 50 fL, from about 100 pL to about 100fL.

In certain aspects, the mean volume of the polydisperse droplets changesby less than 50%, less than 40%, less than 35%, less than 30%, less than25%, less than 20%, less than 15%, less than 10%, less than 5%, lessthan 4%, less than 3%, less than 2%, or less than 1% during amplifyingthe sample. In other aspects, the median volume of the polydispersedroplets changes by less than about 50%, less than about 40%, less thanabout 35%, less than about 30%, less than about 25%, less than about20%, less than about 15%, less than about 10%, less than about 5%, lessthan about 4%, less than about 3%, less than about 2%, or less thanabout 1% during amplifying the sample.

In some aspects, the amplifying the sample comprises a firstamplification cycle, and wherein fewer than 50%, fewer than 45%, fewerthan 40%, fewer than 35%, fewer than 30%, fewer than 25%, fewer than20%, fewer than 19%, fewer than 18%, fewer than 17%, fewer than 16%,fewer than 15%, fewer than 14%, fewer than 13%, fewer than 12%, fewerthan 11%, fewer than 10%, fewer than 9%, fewer than 8%, fewer than 7%,fewer than 6%, fewer than 5%, fewer than 4%, fewer than 3%, fewer than2%, or fewer than 1% of the polydisperse droplets fuse after the firstamplification cycle. In further aspects, the amplifying the samplecomprises a first amplification cycle, and wherein fewer than about 50%,fewer than about 45%, fewer than about 40%, fewer than about 35%, fewerthan about 30%, fewer than about 25%, fewer than about 20%, fewer thanabout 19%, fewer than about 18%, fewer than about 17%, fewer than about16%, fewer than about 15%, fewer than about 14%, fewer than about 13%,fewer than about 12%, fewer than about 11%, fewer than about 10%, fewerthan about 9%, fewer than about 8%, fewer than about 7%, fewer thanabout 6%, fewer than about 5%, fewer than about 4%, fewer than about 3%,fewer than about 2%, or fewer than about 1% of the polydisperse dropletsfuse after the first amplification cycle.

In some aspects, the refractive index of the first fluid differs fromthe refractive index of the second fluid by less than 200%, less than100%, less than 60%, less than 50%, less than 45%, less than 40%, lessthan 35%, less than 30%, less than 25%, less than 20%, less than 19%,less than 18%, less than 17%, less than 16%, less than 15%, less than14%, less than 13%, less than 12%, less than 11%, less than 10%, lessthan 9%, less than 8%, less than 7%, less than 6%, less than 5%, lessthan 4%, less than 3%, less than 2%, or less than 1%. In furtheraspects, the refractive index of the first fluid differs from therefractive index of the second fluid by less than about 200%, less thanabout 100%, less than about 60%, less than about 50%, less than about45%, less than about 40%, less than about 35%, less than about 30%, lessthan about 25%, less than about 20%, less than about 19%, less thanabout 18%, less than about 17%, less than about 16%, less than about15%, less than about 14%, less than about 13%, less than about 12%, lessthan about 11%, less than about 10%, less than about 9%, less than about8%, less than about 7%, less than about 6%, less than about 5%, lessthan about 4%, less than about 3%, less than about 2%, or less thanabout 1%.

In some aspects, such as in double emulsions, the refractive index ofthe first fluid differs from the refractive index of the bulk medium byless than 200%, less than 100%, less than 60%, less than 50%, less than45%, less than 40%, less than 35%, less than 30%, less than 25%, lessthan 20%, less than 19%, less than 18%, less than 17%, less than 16%,less than 15%, less than 14%, less than 13%, less than 12%, less than11%, less than 10%, less than 9%, less than 8%, less than 7%, less than6%, less than 5%, less than 4%, less than 3%, less than 2%, or less than1%.

In some aspects, the polydisperse droplets comprise a plurality ofemulsions. In certain aspects, the plurality of emulsions is prepared bycombining three or more immiscible fluids.

Devices and Methods for Performing Digital Measurements

Another aspect of the disclosure comprises a device for carrying out themethods of the disclosure. According to this aspect, the presentdisclosure provides a means for producing an plurality of polydispersedroplets having a volume distribution, a means for measuring the volumeof a given droplet in the plurality of polydisperse droplets, a meansfor determining the presence or absence of sample in the droplet, andthe concentration of sample in the plurality of polydisperse droplets.The present methods enable the performance of digital measurements overa large dynamic range and methods and systems for increasing the dynamicrange. Specifically, the device increases the dynamic range of digitalmeasurements of a sample by, inter alia, creating sample volumes ofdifferent sizes.

In various aspects, the present disclosure provides methods forperforming a digital assay, comprising: producing a plurality ofpolydisperse droplets, wherein at least some of the droplets comprise asample; amplifying the sample; labeling the sample with a detectableagent; obtaining an image stack for a droplet; determining from theimage stack the volume of the droplet; determining from the image stackthe presence or absence of the detectable agent in the droplet; anddetermining the concentration of the sample in the plurality of dropletsbased on the presence or absence of the detectable agent in theplurality of droplets.

In some aspects, obtaining the image stack comprises optical imaging. Insome aspects, detecting the detectable agent comprises optical imaging.

In further aspects, the optical imaging is performed by confocalmicroscopy, line confocal microscopy, deconvolution microscopy, spinningdisk microscopy, multi-photon microscopy, planar illuminationmicroscopy, Bessel beam microscopy, differential interference contrastmicroscopy, phase contrast microscopy, epifluorescence microscopy,bright field imaging, dark field imaging, oblique illumination, or acombination thereof.

In certain aspects, the image stack comprises a plurality of imagestaken from separate depths of focus through a single droplet.

In further aspects, the image stack comprises 2, 3, 4, 5, 6, 7, 8, 9,10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95or 100 images taken from separate depths of focus for a droplet. Inother aspects, the image stack comprises greater than 2, greater than 3,greater than 4, greater than 5, greater than 6, greater than 7, greaterthan 8, greater than 9, greater than 10, greater than 15, greater than20, greater than 25, greater than 30, greater than 35, greater than 40,greater than 45, greater than 50, greater than 55, greater than 60,greater than 65, greater than 70, greater than 75, greater than 80,greater than 85, greater than 90, greater than 95 or greater than 100images taken from separate depths of focus for a droplet. In still otheraspects, the image stack comprises greater than about 2, greater thanabout 3, greater than about 4, greater than about 5, greater than about6, greater than about 7, greater than about 8, greater than about 9,greater than about 10, greater than about 15, greater than about 20,greater than about 25, greater than about 30, greater than about 35,greater than about 40, greater than about 45, greater than about 50,greater than about 55, greater than about 60, greater than about 65,greater than about 70, greater than about 75, greater than about 80,greater than about 85, greater than about 90, greater than about 95 orgreater than about 100 images taken from separate depths of focus for adroplet.

In further aspects, the image stack comprises from 100 to 50, 100 to 75,100 to 25, 100 to 20, 100 to 10, 100 to 5, 50 to 20, 50 to 10, 50 to 5,20 to 10, 20 to 5, 10 to 5, 10 to 2, about 100 to about 50, about 100 toabout 75, about 100 to about 25, about 100 to about 20, about 100 toabout 10, about 100 to about 5, about 50 to about 20, about 50 to about10, about 50 to about 5, about 20 to about 10, about 20 to about 5,about 10 to about 5, or about 10 to about 2 images taken from separatedepths of focus for a droplet or object planes of the imaging device.

In some aspects, the present methods are performed concurrently on aplurality of droplets. In further aspects, the plurality of polydispersedroplets comprises an array of polydisperse droplets. In yet furtheraspects, the array of polydisperse droplets is disposed in a multi-wellplate.

In some aspects, the volume of the droplets is determined from the imagestack by the Line Scan Method, Simple Boundary Method, Reverse WatershedMethod, Circle Detection Method, Combined Reverse Watershed and CircleDetection Method, or a combination thereof.

In some aspects, the concentration of the detectable agent is determinedover a dynamic range of at least three orders of magnitude or over adynamic range of at least six orders of magnitude.

In some aspects, the plurality of polydisperse droplets comprises afirst fluid and a second fluid, wherein the first fluid is immiscible inthe second fluid. In certain aspects, the emulsion of polydispersedroplets is formed by agitating a solution comprising a first fluid anda second fluid, wherein the first fluid is immiscible in the secondfluid. In further aspects, the agitating comprises vortexing.

In various aspects, the present disclosure provides methods comprising:forming an emulsion of polydisperse droplets by agitating a solutioncomprising a first fluid and a second fluid, wherein the first fluid isimmiscible in the second fluid; and agitating the emulsion in a thirdfluid, wherein the third fluid is immiscible in the second fluid,thereby forming a double emulsion.

In some aspects, the present disclosure provides methods that comprisefluid agitation, wherein the agitating can be shaking, vortexing,sonicating, mixing with magnets, extrusion, via flow focusing or acombination thereof. In further aspects, the agitating is sufficient toform an emulsion. In further aspects, extrusion comprises pipetting thefluid, wherein the pipetting is sufficient to produce an emulsion. Incertain aspects, the agitating occurs in a microfluidic device.

In various aspects, the first fluid comprises water, the second fluidcomprises oil and the third fluid comprises water.

In various aspects, the polydisperse droplets comprise a plurality ofemulsions. In further aspects, the plurality of emulsions is prepared bycombining three or more immiscible fluids.

In some aspects the first fluid is aqueous. In certain aspects, firstfluid comprises a sample. In further aspects, the second fluid is anoil. In certain aspects, the second fluid is an oil, and the secondfluid is immiscible with the first fluid and the third fluid. In someaspects, the first fluid is different from the third fluid. In certainaspects, the third fluid is an oil, and wherein the third fluid isimmiscible with the first fluid and the second fluid.

In some aspects, the emulsion comprises an aqueous phase and anon-aqueous phase. In further aspects, the first fluid comprises waterand the second fluid comprises oil.

In certain aspects, the plurality of polydisperse droplets furthercomprises a fluid interface modification element. In further aspects,the fluid interface modification element is a surfactant. In yet furtheraspects, the fluid interface modification element is selected from alipid, phospholipid, glycolipid, protein, peptide, nanoparticle,polymer, precipitant, microparticle, a molecule with a hydrophobicportion and a hydrophilic portion, or a combination thereof.

In some aspects, the present methods further comprise converting one ormore of the immiscible fluids to a gel or solid. In certain aspects, theimmiscible fluid is converted to a gel or solid before amplifying thesample, during amplifying the sample, or after amplifying the sample.

In various aspects, the detectable agent used in the present methods isfluorescent or luminescent. In certain aspects, the detectable agent isfluorescein, a derivative of fluorescein, rhodamine, a derivative ofrhodamine, or a semiconducting polymer.

As used herein, the term “dynamic range” is defined as the ratio betweenthe largest and smallest possible values of a changeable quantity.

The term “digital assay” means an assay in which measurements are madebased on a counting of smaller measurements, wherein each smallermeasurement is binary, having a value that is one of exactly twopossible values that can be assigned to it. The digital assays describedherein comprise measurements of a sample present in a fluid based on acounting of binary measurements obtained from individual volumes of thefluid.

Reactions (e.g., amplification) can be carried out in volumes withdifferent sizes, before or during analysis of the volumes to determinein which volumes have undergone reaction (e.g., have amplified product).In certain examples, the volumes (e.g., droplets) can be sized and thenumber of occupied droplets (e.g., droplets containing a detectableagent) counted. All or just some of the droplets can be analyzed.Analysis can, for example, be achieved by flowing the droplets in asingle file through a flow cytometer or similar device, where the sizeof the droplet can be determined and the presence of amplification canbe detected. The size of the droplet can, for example, determined basedon the scattering signal from the droplet and the presence ofamplification can be indicated by a fluorescence signal from thedroplet. Alternatively, the diameter of droplets can be determined bymicroscopy. Droplets can be extracted (before, during, or aftercompletion of a reaction, e.g., amplification) from a sample holder andimaged in widefield with a CCD camera. The droplets, e.g., can be spreadout on a surface or embedded between two glass slides and placed under awidefield microscope. By using appropriate excitation and emissionfilters the fluorescence within the droplet can be quantified to revealthe presence or absence of amplification. By noting both the size of thedroplet and the presence or absence of amplification product in eachdroplet, it is possible to back-calculate the original concentration ofthe analyte present in the sample after interrogating a sufficientnumber of droplets of different sizes. Because the droplets are ofdifferent sizes, for a given dynamic range, the analysis is much fasterthan if the droplets are all of similar size. In some aspects, themethods herein further include using a number of droplets in a pluralityand the individual volumes of the droplets in the plurality to conductdigital measurements. For example, a sample concentration of a moleculeof interest can be determined using the number of droplets in theplurality, the number of droplets in the plurality with one or moremolecules of interest, and by measuring the volume of some or all of thedroplets in the plurality. Example methods for determining sampleconcentrations can be found in the Examples section.

In some aspects, the present disclosure provides methods for performinga digital assay, comprising: producing a plurality of polydispersedroplets, wherein at least some of the droplets comprise a sample;amplifying the sample; labeling the sample with a detectable agent;flowing the plurality of polydisperse droplets through a flow cytometrychannel; determining the volume of a droplet as it flows through theflow cytometry channel; determining the presence or absence of thedetectable agent in the droplet; and determining the concentration ofthe sample in the plurality of droplets based on the presence or absenceof the detectable agent in a plurality of droplets.

In certain aspects, determining the concentration of the samplecomprises detecting light scattered from a droplet.

The present disclosure can be used for any technique in which digitalmeasurements provide useful information about a sample. As such, themethods, systems and devices provided herein can include a volumecontaining a detectable agent. In certain aspects, the volume can be awell or chamber in a microfluidic chip or a droplet (e.g., a waterdroplet formed in an emulsion or on the surface of a chip) that containsthe detectable agent. It will be generally understood that thedetectable agent can include a single detectable molecule or a pluralityof detectable molecules. Other types of detectable agents can be used,e.g., beads, quantum dots, nanoparticles, and the like. Furthermore, thedetectable agent can, for example, be a molecule of interest present ina sample to be analyzed (e.g., a nucleic acid molecule in blood, serum,saliva or other solutions). Alternatively, a detectable agent can be amolecule that associates with a molecule of interest (e.g., the nucleicacid molecule) in the sample, thereby allowing the molecule to bedetected. In some aspects, the methods and systems of the presentdisclosure can be used for amplification-related techniques (e.g.,digital PCR) involving digital measurements. For amplificationmeasurements, a volume (e.g., a droplet) can include a single DNAmolecule, for example, but the volume will also contain necessarycomponents that are generally well known to be used for amplificationand detection. In some aspects, the detectable agent is fluorescent and,thus, can be detected by fluorescence-based detection methods known inthe art. However, other detection methods (e.g., absorbance,chemiluminescence, turbidity, and/or scattering) can be used to analyzethe contents of a volume. A variety of detectable agents suitable forthe present disclosure are generally well known in the art and can, forexample, be found in The Molecular Probes Handbook, 11^(th) Edition(2010).

In certain aspects, the detectable agent can be associated with amolecule of interest for detection. For example, the detectable agentcan be associated with a nucleic acid molecule (e.g., DNA or RNA), apeptide, a protein, a lipid, or other molecule (e.g., biomolecule)present in a sample. As defined herein, “associated” in the context ofthe detectable agent includes interaction with the molecule via covalentand/or non-covalent interactions. For example, the detectable agent canbe covalently attached to the molecule of interest. Alternatively, thedetectable agent can, for example, be an intercalation agent or a Taqmanprobe that can be used to detect a nucleic acid molecule (e.g., a DNAand/or RNA molecule). Other detectable agents can be used, such asreference dyes that may not associate with molecules in a volume ofinterest. The present disclosure further includes determining aconcentration of a sample. For example, the methods and systems can beused to determine (1) volumes of droplets and (2) a number of dropletsthat contain a detectable agent, which can be used to determine theconcentration of a sample (i.e., by determining the presence or absenceof a sample in a given droplet). This information can be used in avariety of ways to determine sample concentrations. For example, targetmolecules are present in the sample at a concentration in units ofmolecules/volume. The sample can be distributed into droplets ofvariable volumes that can be analyzed. The individual volumes of thedroplets (all or just some) can be determined by methods providedherein. In addition, using detection methods described herein, dropletscan be analyzed for containing a detectable agent or not. For a givensample concentration, some of the variable-volume droplets can contain adetectable agent and some may not. For higher sample concentrations,generally more droplets of a plurality will contain detectable agentsand vice versa; for low sample concentrations, fewer droplets of aplurality can be occupied by a detectable agent. As further describedherein, the probabilities of occupancy by a detectable agent in aparticular volume distribution can be defined for a wide range of sampleconcentrations, which can then be compared to real data to determine theconcentration of an unknown sample. Additional disclosure fordetermining sample concentrations can be found in EXAMPLE 8 below. Themethods illustrated in EXAMPLE 8 involve making an initial estimate forthe sample concentration and then calculating the number of dropletsthat would be predicted to contain one or more detectable agents(occupied droplets). The estimate for the sample concentration is thenadjusted using a well-known numerical method until the predicted numberof occupied droplets equals the actual number of occupied droplets inthe plurality to within the desired degree of accuracy.

In some aspects, the methods of the present disclosure comprisemeasuring a volume of a droplet only if the droplet comprises a sample.In further aspects, the methods comprise excluding from measurement anydroplets determined to not comprise the sample. In some aspects, sampleconcentrations are determined according to methods disclosed herein byidentifying, sizing or enumerating only those droplets, which aredetermined to comprises sample. In some aspects, sample concentration isdetermined by measuring or knowing the total volume of the sample and byidentifying, sizing and enumerating only those droplets, which aredetermined to comprises sample. In further aspects, the concentrationsof analytes in a sample is determined by measuring or knowing the totalvolume of the sample and by enumerating all the positive droplets anddetermining the volume of each positive droplet. Advantages of thismethod include reducing the number of droplets scanned and therebyreducing the analysis time for determining sample concentration.

As further described herein, the present disclosure provides variousaspects for digital measurements that cannot be achieved by existingmethods and systems. For example, the present disclosure can provide theability to measure sample concentration over a wide dynamic range. Insome aspects, the dynamic range can be at least three orders ofmagnitude, at least four orders of magnitude, at least five orders ofmagnitude, or at least six orders of magnitude. In some aspects, thedynamic range can be between about 10 and 10¹⁰ molecules/mL, about 10²and 10⁷ molecules/mL, about 10⁴ and 10¹⁰ molecules/mL, about 10⁵ and 10⁹molecules/mL. In certain aspects, determining sample concentrationwithin a dynamic range can be performed by detecting a detectable agentthat is associated with a molecule of interest in the sample. Dynamicrange can be dependent on a variety of factors, such as the range ofvolumes that are produced in an emulsion and/or the range of volumesthat are analyzed and detected. In certain aspects, the volumedistributions include continuously varying droplet volumes.

In some aspects, the present methods are performed on a chip usingconcentration gradients. By integrating dPCR with on-chip gradientgeneration, or by using digitized volumes of varying sizes, or thecombination of both these methods, the disclosure effectively increasesthe dynamic range of our dPCR chip by one order to six orders ofmagnitude, which is comparable to the dynamic range offered by RT-PCR.By using a greater range of concentration gradients or arrays ofdigitized volumes with larger size differences, the dynamic range can beincreased even further if desired. This method for carrying outquantitative PCR (qPCR) offers several key advantages over existingtechnologies: (1) it is more accurate; (2) it obviates the need forrunning the type of calibration samples that are needed for RT-PCR andthus is higher throughput; and (3) it removes the need for real-timesensitive fluorescence detection, which is responsible for therelatively higher cost (˜10×) of RT-PCR versus standard PCR devices.

Another aspect of the disclosure comprises a device for carrying out themethods of the disclosure, wherein the device creates arrays ofdigitized and discrete volumes of different sizes. In another aspect,the device carries out the method for increasing the dynamic range ofdigital measurements of a sample, comprising creating a sampleconcentration gradient and creating sample volumes of different sizes.

In some aspects, the present disclosure provides methods for usingdigital measurements to determine a concentration of a sample. Themethods can include producing a plurality of droplets having a volumedistribution, wherein at least one of the droplets of the pluralitycontains contents from the sample; determining the volume of thedroplets; determining the presence of absence of sample in the droplets;and using the volumes of the droplets and the number of droplets foundto contain the detectable agent to determine the concentration of thesample.

In some aspects, the present disclosure includes methods to increase thedynamic range of digital measurements that are based on creating arraysof digitized and discrete volumes of varied sizes (i.e., volumes). Thismethod is better than simply increasing the number of digitized volumesso as to increase dynamic range. This is because simply increasing thenumber of digitized volumes increases the area the volumes occupy aswell as increase the likelihood of having defects on the chip where somedigitized volumes do not form properly or have other defects. Simplyincreasing the number of digitized volumes also decreases throughput byincreasing the time required to analyze all the digitized volumes. Incertain aspects, dynamic range can be increased by creating arrays ofdigitized volumes of different sizes rather than simply increasing thenumber of digitized volumes. The arrays of digitized volumes ofdifferent sizes can be a random array (e.g., droplets of differentdiameters all present and distributed randomly in a container) or can bea regular array.

Sample Amplification

The present disclosure also provides methods, devices, and systems forthe amplification of samples, such as e.g., nucleic acid samples. Incertain aspects, sample amplification comprises PCR. In further aspects,sample amplification comprises dPCR.

In various aspects, the sample comprises a nucleotide. In variousaspects, amplifying the sample comprises performing polymerase chainreaction (PCR), rolling circle amplification (RCA), nucleic acidsequence based amplification (NASBA), loop-mediated amplification(LAMP), or a combination thereof. In further aspects, amplifying thesample comprises isothermal amplification of nucleotides or variabletemperature amplification of nucleotides.

Any suitable device can be used to perform amplification according tothe present disclosure. A variety of device features can be included,such as for example, a means for maintaining or cycling temperature,which can be used to enable the performance of PCR-based amplification.Other device features can include, without limitation, warm-water baths,incubators, and other heat sources, as well as insulators for trappingheat into a confined volume.

In various aspects, the present disclosure provides methods, devices,and systems for performing homogenous assays. As used herein, the term“homogeneous assay” refers to an assay in which all assay componentsexist in solution phase at the time of detection. In a homogeneousassay, no component of the assay scatters detectable light.

In further aspects, the present disclosure provides methods, devices,and systems for performing non-homogenous assays. As used herein, theterm “non-homogeneous assay” refers to an assay in which one or moreassay components are present in solid phase at the time of detection.The term non-homogenous assay is used interchangeably with the term“heterogeneous assay.” Formation of a precipitate or particulate, suchas in LAMP or rolling circle amplification, is a common form of aheterogeneous assay. In this type of assay, the solid-phase componentscan scatter detectable light.

In various aspects, the present disclosure provides methods, devices,and systems for amplification by performing digital PCR (dPCR). DigitalPCR is a method in which individual nucleic acid molecules present in asample are distributed to many separate reaction volumes (e.g., chambersor aliquots) prior to PCR amplification of one or more target sequences.The concentration of individual molecules in the sample is adjusted sothat at least some of the reaction volumes contain no target moleculesand at least some of the reaction volumes contain at least one targetmolecule. Amplification of a target sequence results in a binary digitaloutput in which each chamber is identified as either containing or notcontaining the PCR product indicative of the presence of thecorresponding target sequence. A count of reaction volumes containingdetectable levels of PCR end-product is a direct measure of the absolutenucleic acids quantity. In various aspects of the present disclosure,nucleic acid samples are distributed by partitioning them into separatereaction volumes. The digitized samples are then thermocycled in thepresence of PCR reagents, thereby facilitating the amplification of thenucleic acid sample.

In a further aspect of the present disclosure, the methods, systems anddevices described herein can be applied to isothermal amplificationtechniques, such as digital ELISA, NASBA, and LAMP. ELISA is proteinbased and usually used for the quantification of proteins or smallmolecules. NASBA and LAMP are isothermal amplification schemes that havebeen developed to complement PCR.

In an isothermal amplification, there is no temperature cyclingoccurring as in traditional PCR. There are several types of isothermalnucleic acid amplification methods such as transcription mediatedamplification, nucleic acid sequence-based amplification, signalmediated amplification of RNA technology, strand displacementamplification, rolling circle amplification, loop-mediated isothermalamplification of DNA, isothermal multiple displacement amplification,helicase-dependent amplification, single primer isothermalamplification, and circular helicase-dependent amplification.

NASBA (Nucleic Acid Sequence Based Amplification) is an isothermal (˜40°C.) process for amplifying RNA, and has been used successfully atdetecting both viral and bacterial RNA in clinical samples. Theadvantages offered by NASBA are: (1) It has high amplificationefficiency and fast amplification kinetics, where over thousand foldamplification can be achieved within an hour or two; (2) It does notgive false positives caused by genomic dsDNA, as in the case of RT-PCR;(3) Gene expression studies can be performed without the use of intronflanking primers; (4) It does not require the degree of temperaturecontrol and feedback needed for PCR. As a result, NASBA has becomepopular for detecting viral and bacterial RNA. The fact that NASBA is anisothermal method makes it possible to run multiple samplessimultaneously with the use of a temperature controlled oven, which isan important practical advantage in many field works.

LAMP, which stands for Loop-Mediated Isothermal Amplification, iscapable of amplifying DNA with high specificity, efficiency, andrapidity under isothermal conditions (˜60° C.). Because of thecharacteristics of its amplification reaction, LAMP is able todiscriminate single nucleotide differences during amplification. As aresult, LAMP has been applied for SNP (single nucleotide polymorphism)typing. LAMP has also been shown to have about 10 fold highersensitivity then RT-PCR in the detection of viruses. Additionally,because LAMP amplification of DNA can be directly correlated with theproduction of magnesium pyrophosphate, which increases the turbidity ofsolution, the progress of LAMP has been monitored using a simpleturbidimeter. Therefore, a non-homogenous assay can be used fordetecting the amplification products that result from LAMP.

In one aspect, the present disclosure provides a method for performingdigital loop-mediated amplification of a sample. The method can includeproducing a plurality of droplets of the sample on a microfluidicdevice, wherein at least one droplet in the plurality comprises anucleic acid molecule (e.g., a DNA and/or a RNA molecule); andperforming loop-mediated amplification in the at least one droplet toproduce amplified product of the nucleic acid molecule. The method canalso include detecting the amplified product. In some aspects, themethod includes determining a number of droplets in the plurality thatcomprise the amplified product; and calculating a concentration of thenucleic acid molecule in the sample using individual volumes of thedroplets in the plurality and the number of droplets in the pluralitythat contain the nucleic acid molecule. The microfluidic device caninclude a plurality of chambers configured to form the plurality ofdroplets.

Despite some of the advantages offered by NASBA and LAMP, one importantdrawback is the difficulty with performing quantification in theconventional real-time fashion or in bulk, which would be beneficial inmost situations. Quantification often requires meticulous calibrationand control using standards amplified under identical conditions, whichcan be very tedious (especially for field studies) and is not practicalin many cases. For non-homogenous assays, such as the detection ofprecipitate in LAMP, accurate calibration can be especially challenging.This issue is effectively addressed with the present digital method thatemploys end-point detection.

Rolling circle amplification (RCA) is an isothermal nucleic-acidamplification method. It differs from the polymerase chain reaction andother nucleic-acid amplification schemes in several respects. DuringRCA, a short DNA probe anneals to a target DNA of interest, such as theDNA of a pathogenic organism or a human gene containing a deleteriousmutation. The probe then acts as a primer for a Rolling CircleAmplification reaction. The free end of the probe anneals to a smallcircular DNA template. A DNA polymerase is added to extend the primer.The DNA polymerase extends the primer continuously around the circularDNA template generating a long DNA product that consists of manyrepeated copies of the circle. By the end of the reaction, thepolymerase generates many thousands of copies of the circular template,with the chain of copies tethered to the original target DNA. Thisallows for spatial resolution of target and rapid amplification of thesignal. The use of forward and reverse primers can change the abovelinear amplification reaction into an exponential mode that can generateup to 10¹² copies in 1 hour. The calibration required for suchquantitative measurements can be cumbersome.

To overcome this drawback, the present disclosure provides digitalisothermal amplifications, such as NASBA and LAMP, where the use of anarray of digitized volumes, similar to digital PCR, is used for carryingout digital NASBA, digital LAMP, and rolling circle amplification.Furthermore, by using concentration gradients and/or arrays of digitizedvolumes of different sizes, we can effectively increase the dynamicrange of these digital measurements. The current method ideallycomplements these isothermal amplification schemes to make them aquantitative technique for measuring the presence of RNA and DNA. Inanother aspect of the disclosure, the method is applied to antibodybased amplification. In another aspect, the method is applied tospecific molecule recognition based amplification.

Various detectable agents can be used according to the presentdisclosure. In various aspects, the detectable agent is fluorescent. Infurther aspects, the detectable agent is luminescent. The detectableagent used can depend on the type of amplification method that isemployed. In one aspect, the signal generation can come from anonsequence specific fluorophore such as EvaGreen or SYBRgreen, wherethe fluorophore is quenched when in solution but can intercalate intodouble-stranded DNA where it exhibits much brighter fluorescence. Thusthe large amount of double stranded DNA generated during PCR results ina significant increase in fluorescence. In another aspect sequencespecific fluorescent probes are used. In one aspect this consists of amolecular beacon such as a hairpin structure, whose fluorescence ishighly quenched in its closed conformation and whose intensity isincreased once it hybridizes to amplified target DNA. In another aspectit consists of a Taqman probe, which hybridizes to the target DNA, andundergoes cleavage of a fluorescent reporter from the probe DNA duringthe next amplification step.

These probes have non-negligible background fluorescence and therelative increase in intensity during amplification can be rather small,depending of the amount of probe added to the reaction. Furthermore, theexcitation intensity can vary across the field of view during thedetection process. In some aspects, a threshold pixel intensity value issubtracted from all pixels in an image to determine whether fluorescenceintensity in a droplet is large enough to indicate the presence of anamplification product. In some aspects, a reference dye, whose spectralsignature can be well separated from the fluorescence probe that reportson amplification, and whose fluorescent signal is insensitive toamplification or other reaction or reagent conditions, can be added toone or more immiscible fluid.

Analysis Methods and Systems

In various aspects, the present disclosure provides methods forperforming a digital assay. A plurality of polydisperse droplets may beproduced. At least some of the droplets may comprise a sample. Thesample may be amplified. The sample may be labeled with a detectableagent. An image stack for a droplet may be obtained. The volume of thedroplet may be determined from the image stack. The presence or absenceof the detectable agent in the droplet may be determined from the imagestack. The concentration of the sample in the plurality of droplets maybe determined based on the presence or absence of the detectable agentin a plurality of droplets.

The image stack may be obtained by optical imaging. The detectable agentmay be detected by optical imaging. The optical imaging may be performedin many ways such as by confocal microscopy, line confocal microscopy,deconvolution microscopy, spinning disk microscopy, multi-photonmicroscopy, planar illumination microscopy, Bessel beam microscopy,differential interference contrast microscopy, phase contrastmicroscopy, epifluorescence microscopy, bright field imaging, dark fieldimaging, oblique illumination, or a combination thereof. In someaspects, the optical imaging comprises the use of adaptive optics andimaging.

The image stack may comprise a plurality of images taken from separatedepths of focus through a single droplet. The image stack may comprise2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65,70, 75, 80, 85, 90, 95 or 100 images taken from separate depths of focusfor a droplet.

The methods of the present disclosure may be performed concurrently on aplurality of droplets. The plurality of polydisperse droplets maycomprise an array of polydisperse droplets. The array of polydispersedroplets may be disposed in a multi-well plate.

The volume of the droplet may be determined from the image stack in manyways such as by the Line Scan Method, Simple Boundary Method, ReverseWatershed Method, Circle Detection Method, Combined Reverse Watershedand Circle Detection Method, or a combination thereof. The concentrationof the detectable agent may be determined over a dynamic range of atleast three orders of magnitude or over a dynamic range of at least sixorders of magnitude.

The plurality of polydisperse droplets may comprise a first fluid and asecond fluid. The first fluid may be immiscible in the second fluid. Anemulsion of polydisperse droplets may be formed by agitating a solutioncomprising a first fluid and a second fluid, wherein the first fluid isimmiscible in the second fluid. To form the emulsion of polydispersedroplets, a solution comprising a first fluid and a second fluid may beagitated. The first fluid may be immiscible in the second fluid. Theemulsion may be agitated in a third fluid. The third fluid may beimmiscible in the second fluid, thereby forming a double emulsion. Thefluid(s) may be agitated in many ways such as shaking, vortexing,sonicating, mixing with magnets, extrusion, flow focusing or acombination thereof. The agitation may be sufficient to form anemulsion. Extrusion, for example, may comprise pipetting the fluid,wherein the pipetting is sufficient to produce the emulsion. Theagitating may occur in a microfluidic device. The agitation may be, forexample, vortexing. The emulsion produced may comprise an aqueous phaseand a non-aqueous phase. The first fluid may comprise water and thesecond fluid may comprise oil. The first fluid may comprise water, thesecond fluid may comprise oil, and the third fluid may comprise water.

The plurality of polydisperse droplets may comprise a plurality ofemulsions. The plurality of emulsions may be prepared by combining threeor more immiscible fluids. The first fluid may be aqueous. The firstfluid may comprise sample. The second fluid may comprise an oil. Thesecond fluid may comprise an oil and the second fluid may be immisciblewith the first fluid and the third fluid. The first fluid may bedifferent from the third fluid. The third fluid may comprise an oil andthe third fluid may be immiscible with the first fluid and the secondfluid.

The plurality of polydisperse droplets may further comprise a fluidinterface modification element. The fluid interface modification elementmay comprise a surfactant. The fluid interface modification element maybe selected from a lipid, phospholipid, glycolipid, protein, peptide,nanoparticle, polymer, precipitant, microparticle, a molecule with ahydrophobic portion and a hydrophilic portion, or a combination thereof.

One or more of the immiscible fluids may be converted to a gel or solid.The immiscible fluid may be converted to a gel or solid beforeamplifying the sample, during amplifying the sample, or after amplifyingthe sample.

The detectable agent may be fluorescent or luminescent. The detectableagent may comprise one or more of fluorescein, a derivative offluorescein, rhodamine, a derivative of rhodamine, or a semiconductingpolymer. The sample may comprise a nucleotide.

To amplify the sample, polymerase chain reaction (PCR), rolling circleamplification (RCA), nucleic acid sequence based amplification (NASBA),loop-mediated amplification (LAMP), or a combination thereof may beperformed. Alternatively or in combination, the sample may be amplifiedby isothermal amplification of nucleotides or variable temperatureamplification of nucleotides.

The distribution of droplet diameters may have a standard deviationgreater than 1000%, greater than 500%, greater than 100%, greater than50%, greater than 30%, greater than 20%, greater than 15%, greater than10%, greater than 9%, greater than 8%, greater than 7%, greater than 6%,or greater than 5% of the median droplet diameter. Alternatively or incombination, the distribution of droplet diameters may have a standarddeviation greater than 1000%, greater than 500%, greater than 100%,greater than 50%, greater than 30%, greater than 20%, greater than 15%,greater than 10%, greater than 9%, greater than 8%, greater than 7%,greater than 6%, or greater than 5% of the mean droplet diameter.

The volumes in the polydisperse droplets may vary by more than a factorof 2, by more than a factor of 10, by more than a factor of 100, by morethan a factor of 1000, by more than a factor of 10000, by more than afactor of 100000, by more than a factor of 1000000, by more than afactor of about 2, by more than a factor of about 10, by more than afactor of about 100, by more than a factor of about 1000, by more than afactor of about 10000, by more than a factor of about 100000, or by morethan a factor of 1000000. The polydisperse droplets may have a volumedistribution of from 100 nanoliters (nL) to 1 femtoliters (fL), from 10nL to 10 fL, from 1 nL to 100 fL, from 100 nL to 1 pL, from 10 nL to 10pL, or from 1 nL to 1 pL, from about 500 pL to about 50 fL, from about100 pL to about 100 fL. The mean volume of the polydisperse droplets maychange by less than 50%, less than 40%, less than 35%, less than 30%,less than 25%, less than 20%, less than 15%, less than 10%, less than5%, less than 4%, less than 3%, less than 2%, or less than 1% duringamplifying the sample.

Amplifying the sample may comprise a first amplification cycle, andfewer than 50%, fewer than 45%, fewer than 40%, fewer than 35%, fewerthan 30%, fewer than 25%, fewer than 20%, fewer than 19%, fewer than18%, fewer than 17%, fewer than 16%, fewer than 15%, fewer than 14%,fewer than 13%, fewer than 12%, fewer than 11%, fewer than 10%, fewerthan 9%, fewer than 8%, fewer than 7%, fewer than 6%, fewer than 5%,fewer than 4%, fewer than 3%, fewer than 2%, or fewer than 1% of thepolydisperse droplets may fuse after the first amplification cycle.

The refractive index of the first fluid may differ from the refractiveindex of the second fluid by less than 200%, less than 100%, less than60%, less than 50%, less than 45%, less than 40%, less than 35%, lessthan 30%, less than 25%, less than 20%, less than 19%, less than 18%,less than 17%, less than 16%, less than 15%, less than 14%, less than13%, less than 12%, less than 11%, less than 10%, less than 9%, lessthan 8%, less than 7%, less than 6%, less than 5%, less than 4%, lessthan 3%, less than 2%, or less than 1%.

In various aspects, the present disclosure provides methods forperforming a digital assay. A plurality of polydisperse droplets may beproduced. At least some of the droplets may comprise a sample. Thesample may be amplified. The sample may be labeled with a detectableagent. The plurality of polydisperse droplets may be flowed through aflow cytometry channel. The volume of a droplet may be determined as itflows through the flow cytometry channel. The presence or absence of thedetectable agent in the droplet may be determined. The concentration ofthe sample in the plurality of droplets may be determined based on thepresence or absence of the detectable agent in the plurality ofpolydisperse droplets. In some aspects, the size of the droplet and/orconcentration of the sample in the droplet may be determined bydetecting light scattered from the droplet.

In various aspects, the present disclosure provides compositions forperforming digital assays. A composition may comprise a first fluid, asecond fluid, a surfactant, and an amplification reagent. The firstfluid and the second fluid may be immiscible in each other and may becapable of forming an emulsion when agitated. In some aspects, thecomposition may further comprise a sample, such as a nucleotide, and/ora detectable agent capable of labeling the sample. The sample may belabeled with the detectable agent.

The composition may further comprise a detectable agent capable ofbinding a nucleic acid sample.

The amplification reagent of the composition may be selected from apolymerase chain reaction (PCR) reagent, rolling circle amplification(RCA) reagent, nucleic acid sequence based amplification (NASBA)reagent, loop-mediated amplification (LAMP) reagent, or a combinationthereof. The amplification reagent may comprise a PCR reagent such as athermostable DNA polymerase, a nucleotide, a primer, probe or acombination thereof.

The composition may further comprise a third fluid. The third fluid maybe immiscible in the second fluid. The composition may be capable offorming a double emulsion. The first fluid may be aqueous. The firstfluid may comprise the amplification reagent. The second fluid maycomprise an oil. The second fluid may be immiscible with the first fluidand the third fluid. The first fluid may be different from the thirdfluid. The third fluid may comprise an oil and may be immiscible withthe first fluid and the second fluid.

The composition may further comprise a fluid interface modificationelement. The fluid interface modification element may comprise asurfactant. The fluid interface modification element may be selectedfrom a lipid, phospholipid, glycolipid, protein, peptide, nanoparticle,polymer, precipitant, microparticle, a molecule with a hydrophobicportion and a hydrophilic portion, or a combination thereof.

The composition may further comprise a solidifying or gelling agentcapable of converting one or more of the immiscible fluids to a gel orsolid.

In some aspects, the present disclosure provides kits for performing adigital assay comprising any of the aforementioned compositions.

In various aspects, the present disclosure provides systems fordetermining a volume of a droplet(s). The system may comprise acontainer, an imaging source, and a computing device. The container maybe configured for holding the droplet(s). The imaging source may beconfigured to obtain an image of the droplet(s) in the container. Thecomputing device may comprise a processor and a memory (e.g., anon-transitory, tangible computer-readable storage medium such as a ROM,RAM, flash memory, or the like). The memory may store a set ofinstructions that when executed by the processor cause (i) the imagingsource to obtain an image stack of the droplet(s) and (ii) the processorto determine the volume of the droplet(s) in the sample based on theobtained image stack.

The droplet(s) may comprise a plurality of droplets. The plurality ofdroplets may be polydisperse. The container may comprise a multi-wellplate.

The imaging source may comprise an optical imaging source. The opticalimaging source may be configured to perform confocal microscopy, lineconfocal microscopy, deconvolution microscopy, spinning disk microscopy,multi-photon microscopy, planar illumination microscopy, Bessel beammicroscopy, differential interference contrast microscopy, phasecontrast microscopy, epiflouorescent microscopy, bright field imaging,dark field imaging, oblique illumination, or a combination thereof.

The image stack for the droplet(s) may comprise a plurality of imagestaken from separate depths of focus through the droplet. The image stackmay comprise 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 25, 30, 35, 40, 45, 50,55, 60, 65, 70, 75, 80, 85, 90, 95 or 100 images taken from separatedepths of focus for the droplet.

The set of instructions when executed by the processor may cause theprocessor to determine the volume of the droplet(s) by (i) identifying apixel set(s) in an individual image of the image stack, (ii) identifyingthe pixel set(s) as at least a part of at least one droplet, (iii)identifying an individual droplet(s) from the pixel set(s) based on thecorrespondence, and (iv) determining the volume of the identifieddroplet(s) based on the pixel set(s). The at least at part of the atleast one droplet may comprise a single droplet, parts of multipledroplets, a single whole droplet, a plurality of whole droplets, orcombinations thereof.

The set of instructions when executed by the processor may cause theprocessor to determine a plurality of volumes of a plurality of dropletsbased on the obtained image stack. The set of instructions when executedby the processor may further cause the processor to determine thepresence or absence of a detectable agent in at least some of theplurality of droplets. The set of instructions when executed by theprocessor may further cause the processor to determine the concentrationof a sample in the plurality of droplets based on the presence orabsence of the detectable agent in the plurality of droplets and thedetermined plurality of volumes of the plurality of droplets. The samplemay comprise a nucleotide. The detectable agent may be fluorescent orluminescent. The detectable agent may comprise fluorescein, a derivativeof fluorescein, rhodamine, a derivative of rhodamine, or asemiconducting polymer.

The plurality of droplets may comprise a sample comprising a nucleotide.The sample in the plurality of droplets may have been amplified. Thesample in the plurality of droplets may have been amplified byperforming polymerase chain reaction (PCR), digital polymerase chainreaction (dPCR), rolling circle amplification (RCA), nucleic acidsequence based amplification (NASBA), loop-mediated amplification(LAMP), or a combination thereof. The sample may have been amplified byisothermal amplification of nucleotides or variable temperatureamplification of nucleotides. The set of instructions when executed bythe processor may cause a concentration of the detectable agent to bedetermined over a dynamic range of at least three orders of magnitude orover a dynamic range of at least six orders of magnitude.

In various aspects, the present disclosure provides methods fordetermining a volume of a droplet. An image stack of the droplet may beobtained. A pixel set(s) in an individual image of the image stack maybe identified. The pixel set(s) may be identified as corresponding to atleast a part of at least one droplet, which may comprise a part of asingle droplet, parts of multiple droplets, a whole droplet, a pluralityof whole droplets, or combinations thereof. Individual droplet(s) may beidentified from the pixel set(s) based on the correspondence. The volumeof the identified individual droplet(s) may be determined based on thepixel set(s).

The image stack of the sample may be obtained by obtaining a pluralityof images taken from separate depths of focus through a droplet(s). 2,3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70,75, 80, 85, 90, 95 or 100 images may be taken from separate depths offocus for the droplet(s).

The volume of the identified droplet(s) may be determined by determiningthe diameter of the identified droplet(s) by using at least one image ofthe image stack in the following ways, alone or in various combinations.One, the identified droplet(s) may be correlated between a plurality ofimages of the image stack and a largest diameter of the identifieddroplet(s) in the plurality of images may be measured. Two, a curve maybe fit to a boundary of the identified droplet(s) and the diameter ofthe identified droplet(s) may be interpolated based on the fitted curve.Three, the diameters of the identified droplet(s) may be correlatedbetween a plurality of images of the image stack, the diameter of theidentified droplet(s) may be identified in each image, and the diameterof the identified droplet(s) may be determined from its diameters in theplurality of images of the image stack. Four, the identified droplet(s)may be correlated between a plurality of images of the image stack, thediameter of the identified droplet(s) may be determined in each image,and the diameter of the identified droplet(s) may be determined from itsdiameters in the plurality of images of the image stack and a differencein image depth between the plurality of images. Other ways ofdetermining the diameter of the identified droplet(s) are alsocontemplated and are within the scope of the present disclosure.

The volumes of a plurality of droplets may be determined. The presenceor absence of a detectable agent in the plurality of droplets may bedetermined from the image stacks. The concentration of a sample in theplurality of droplets may be determined based on the presence or absenceof the detectable agent in the plurality of droplets and the determinedvolumes of the plurality of droplets.

The sample may comprise a nucleotide. The sample in the plurality ofdroplets may be amplified in many ways such as by performing polymerasechain reaction (PCR), rolling circle amplification (RCA), nucleic acidsequence based amplification (NASBA), loop-mediated amplification(LAMP), or a combination thereof. Alternatively or in combination, thesample may be amplified by isothermal amplification of nucleotides orvariable temperature amplification of nucleotides.

The concentration of the detectable agent may be determined over adynamic range of at least three orders of magnitude or over a dynamicrange of at least six orders of magnitude. The detectable agent may befluorescent or luminescent. The detectable agent may comprisefluorescein, a derivative of fluorescein, rhodamine, a derivative ofrhodamine, or a semiconducting polymer.

The image stack may be obtained by optical imaging. The optical imagingmay be performed by confocal microscopy, line confocal microscopy,deconvolution microscopy, spinning disk microscopy, multi-photonmicroscopy, planar illumination microscopy, Bessel beam microscopy,differential interference contrast microscopy, phase contrastmicroscopy, epifluorescence microscopy, bright field imaging, dark fieldimaging, oblique illumination, or a combination thereof.

An image stack of a plurality of polydisperse droplets may be obtained.The plurality of polydisperse droplets may comprise a first fluid and asecond fluid. The first fluid may be immiscible in the second fluid. Anemulsion of polydisperse droplets may be formed by agitating a solutioncomprising a first fluid and a second fluid. To obtain the image stack,the formed emulsion may be imaged. The first fluid may comprise waterand the second fluid may comprise oil.

Furthermore, an emulsion of polydisperse droplets may be formed byagitating a solution comprising a first fluid and a second fluid. Thefirst fluid may be immiscible in the second fluid. And, the emulsion maybe agitated in a third fluid. The third fluid may be immiscible in thesecond fluid, thereby forming a double emulsion. The first fluid maycomprise water, the second fluid may comprises oil, and the third fluidmay comprises water. The fluid(s) may be agitated in many ways such asby shaking, vortexing, sonicating, mixing with magnets, extruding, flowfocusing or a combination thereof. The agitation may be sufficient toform an emulsion. The extrusion, for example, may comprise pipetting thefluid, wherein the pipetting is sufficient to produce an emulsion. Theagitating may occur in a microfluidic device.

The emulsion may comprise an aqueous phase and a non-aqueous phase. Thepolydisperse droplets may comprise a plurality of emulsions. Thepolydisperse droplets may comprise a plurality of emulsions. Theplurality of emulsions may be prepared by combining three or moreimmiscible fluids. The three or more immiscible fluids may comprise afirst fluid, a second fluid, and a third fluid. The first fluid may beaqueous. The second fluid may comprise an oil. The second fluid may beimmiscible with the first fluid and the third fluid. The immisciblefirst, second, and/or third fluid(s) may be converted into a gel orsolid. The first fluid may be different from the third fluid. The thirdfluid may comprise an oil. The third fluid may be immiscible with thefirst fluid and the second fluid. The immiscible third fluid may beconverted into a solid or gel. The first fluid may comprise a sample fordetection. The refractive index of the first fluid may differs from therefractive index of the second fluid by less than 200%, less than 100%,less than 60%, less than 50%, less than 45%, less than 40%, less than35%, less than 30%, less than 25%, less than 20%, less than 19%, lessthan 18%, less than 17%, less than 16%, less than 15%, less than 14%,less than 13%, less than 12%, less than 11%, less than 10%, less than9%, less than 8%, less than 7%, less than 6%, less than 5%, less than4%, less than 3%, less than 2%, or less than 1%.

The plurality of polydisperse droplets may further comprise a fluidinterface modification element. The fluid interface modification elementmay comprise a surfactant. The fluid interface modification element maybe selected from a lipid, phopholipid, glycolipid, protein, peptide,nanoparticle, polymer, precipitant, microparticle, a molecule with ahydrophobic portion and a hydrophilic portion, or a combination thereof.For example, the fluid interface modification element may comprise aPEG-based surfactant.

The distribution of droplet diameters may have a standard deviationgreater than 1000%, greater than 500%, greater than 100%, greater than50%, greater than 30%, greater than 20%, greater than 15%, greater than10%, greater than 9%, greater than 8%, greater than 7%, greater than 6%,or greater than 5% of the median droplet diameter. The distribution ofdroplet diameters may have a standard deviation greater than 1000%,greater than 500%, greater than 100%, greater than 50%, greater than30%, greater than 20%, greater than 15%, greater than 10%, greater than9%, greater than 8%, greater than 7%, greater than 6%, or greater than5% of the mean droplet diameter.

The volumes in the polydisperse droplets may vary by more than a factorof 2, by more than a factor of 10, by more than a factor of 100, by morethan a factor of 1000, by more than a factor of 10000, by more than afactor of 100000, by more than a factor of 1000000, by more than afactor of about 2, by more than a factor of about 10, by more than afactor of about 100, by more than a factor of about 1000, by more than afactor of about 10000, by more than a factor of about 100000 or by morethan a factor of 1000000.

The polydisperse droplets may have a volume distribution of from 100nanoliters (nL) to 1 femtoliters (fL), from 10 nL to 10 fL, from 1 nL to100 fL, from 100 nL to 1 pL, from 10 nL to 10 pL, or from 1 nL to 1 pL,from about 500 pL to about 50 fL, from about 100 pL to about 100 fL.

The sample may be amplified for detection in the polydisperse droplets.

The mean volume of the polydisperse droplets may change by less than50%, less than 40%, less than 35%, less than 30%, less than 25%, lessthan 20%, less than 15%, less than 10%, less than 5%, less than 4%, lessthan 3%, less than 2%, or less than 1% during amplifying the sample.

Amplifying the sample may comprise a first amplification cycle, andfewer than 50%, fewer than 45%, fewer than 40%, fewer than 35%, fewerthan 30%, fewer than 25%, fewer than 20%, fewer than 19%, fewer than18%, fewer than 17%, fewer than 16%, fewer than 15%, fewer than 14%,fewer than 13%, fewer than 12%, fewer than 11%, fewer than 10%, fewerthan 9%, fewer than 8%, fewer than 7%, fewer than 6%, fewer than 5%,fewer than 4%, fewer than 3%, fewer than 2%, or fewer than 1% of thepolydisperse droplets may fuse after the first amplification cycle.

Further, the pixel set(s) in an individual image of the image stack maybe identified by obtaining a plurality of line scans within theindividual image, setting a threshold level, and identifying an area inthe plurality of the line scans outside the threshold level as the pixelset(s) (e.g., the area may be outside the threshold level if it is belowor above the threshold level). While line scans are generally discussedherein, other methods of generating scans are also contemplated. Thesemethods may include confocal scanning, line illumination and collection,Nipkow disc type scanning, or the like.

To identify one or more droplets in an image, the Simple Boundary methodmay be used. To perform the Simple Boundary Method, one or more pixelsets of the individual image of the image stack above a threshold may beidentified. The pixel set may include a part of a single droplet, partsof multiple droplets, a whole droplet, whole droplets, or combinationsthereof. The pixel set may be identified as corresponding to one dropletby determining an aspect ratio of the pixel set. The pixel set may beidentified as corresponding to one droplet when the aspect ratio of thepixel set is less than or equal to a threshold value. The thresholdvalue may be 1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, or 2.

To identify droplet(s) in an image, a Reverse Watershed Method may beperformed. Performing the Reverse Watershed Method may comprisegenerating a map based on pixel intensities of the individual image ofthe image stack, identifying one or more pixel sets in the generatedmap, identifying an individual pixel set as a region of interest, andfitting a boundary of the region of interest with a best-fit circle. Thepixel set may include a part of a single droplet, parts of multipledroplets, a whole droplet, a plurality of whole droplets, orcombinations thereof. The individual image of the image stack may besmoothed before generating the map. The map generated based on pixelintensities of the individual images of the image stack may comprise atopological map. To identify the one or more pixel set(s), whether anindividual pixel comprises a background pixel or a droplet pixel may bedetermined based on the pixel intensity of the individual pixel and oneor more threshold values. The individual pixel set may be identified asa region of interest when the individual pixel set has an area above aminimum required area. Further, whether the individual pixel setcomprises a plurality of regions of interest may be determined and theplurality of regions of interest may be combined into a single region ofinterest. The region of interest may include a part of a single droplet,parts of multiple droplets, a whole droplet, a plurality of wholedroplets, or combinations thereof.

To identify one or more droplets in an image, a Circle Detection Methodmay be performed. To perform the Circle Detection Method, one or morepixel sets of the individual image of the image stack above a thresholdmay be identified, a plurality of circles may be superimposed over theidentified one or more pixel sets, one or more circles of thesuperimposed plurality of circles may be rejected when the one or morecircles do not meet at least one predetermined criteria, and one or moreremaining circles may be identified as corresponding to the droplet. Thepixel set may include a part of a single droplet, parts of multipledroplets, a whole droplet, a plurality of whole droplets, orcombinations thereof.

To identify one or more droplets in an image, a Combined ReverseWatershed and Circle Detection Method may be performed. To perform theCombined Reverse Watershed and Circle Detection method, a map based onpixel intensities of the individual image of the image stack may begenerated, one or more pixel sets in the map may be identified, anindividual pixel set may be identified as a region of interest, aplurality of circles may be superimposed over the region of interest,one or more circles of the superimposed plurality of circles may berejected when the one or more circles do not meet at least onepredetermined criteria, and one or more remaining circles may beidentified as corresponding to one droplet. The pixel set may include apart of a single droplet, parts of multiple droplets, a whole droplet, aplurality of whole droplets, or combinations thereof. The individualimage of the image stack may be smoothed before generating the map. Themap based on pixel intensities of the individual images of the imagestack may comprise a topological map. To identify the one or more pixelsets, an individual pixel may be identified as a background pixel or adroplet pixel based on the pixel intensity of the individual pixel andone or more threshold values. The region of interest may include a partof a single droplet, parts of multiple droplets, a whole droplet, aplurality of whole droplets, or combinations thereof.

An individual pixel set may be determined to comprise a region ofinterest if the individual pixel set has an area above a minimumrequired area. The at least one predetermined criteria may comprise oneor more of (i) selecting one or more circles that include a largestfraction of external boundary pixels of the region of interest, (ii)selecting one or more circles that include a largest fraction of an areaof the region of interest, (iii) rejecting one or more circles thatinclude pixels from a different pixel group than the region of interest,(iv) rejecting one or more circles that include a substantial number ofnon-group pixels, or (v) discriminating against one or more circles thathave a substantial fraction of their circumference in the interior ofthe pixel group.

To reject the one or more circles, the plurality of super imposedcircles may be examined in pairs. The examined circles may comprise afirst circle and a second circle. Further, one of the first or secondcircles may be rejected based on a vote which may be user-defined.

The one or more remaining circles may be identified as corresponding toone droplet by assigning the one or more remaining circles to onedroplet. The one or more circles may be assigned to one droplet based onone or more of (i) assigning the to the droplet the circle with the bestgoodness of fit statistic to the droplet or (ii) assigning the region ofinterest to the droplet having a largest overlap in area with the one ormore circles of the region of interest.

To determine the volume of the identified droplet based on the region ofinterest, one or more diameters of the one or more identified circlescorresponding to the droplet may be determined.

In various aspects, the present disclosure provides systems forperforming digital assays. The system may comprise a container, animaging source, and a computing device. The container may be configuredfor holding a plurality of polydisperse droplets. At least some of thedroplets may comprise a sample labeled with a detectable agent. Theimaging source may be configured to obtain an image stack of theplurality of polydisperse droplets held in the container. The computingdevice may be configured to operate the imaging source. The computingdevice may comprise a processor and a memory (e.g., a non-transitory,tangible computer-readable storage medium such as a ROM, RAM, flashmemory, or the like). The memory may store a set of instructions thatwhen executed by the processor cause (i) the imaging source to obtainthe image stack of the plurality of polydisperse droplets held in thecontainer, (ii) the processor to determine the volumes of the pluralityof polydisperse droplets based on the obtained image stack, (iii) theprocessor to determine the presence or absence of the detectable agentin the plurality of polydisperse droplets, and (iv) the processor todetermine the concentration of the sample in the plurality of dropletsbased on the presence or absence of the detectable agent in theplurality of polydisperse droplets and the volumes of the plurality ofpolydisperse droplets.

The container may comprise a multi-well plate. The imaging source maycomprises an optical imaging source. The optical imaging source may beconfigured to perform one or more of confocal microscopy, line confocalmicroscopy, deconvolution microscopy, spinning disk microscopy,multi-photon microscopy, planar illumination microscopy, Bessel beammicroscopy, differential interference contrast microscopy, phasecontrast microscopy, epiflouorescent microscopy, bright field imaging,dark field imaging, oblique illumination, or a combination thereof.

The obtained image stack may comprise a plurality of images taken fromseparate depths of focus through a single droplet. The image stack maycomprise 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55,60, 65, 70, 75, 80, 85, 90, 95 or 100 images taken from separate depthsof focus for the single droplet.

The set of instructions when executed by the processor may cause theprocessor to determine the volumes of the plurality of polydispersedroplets by (i) identifying a pixel set(s) in an individual image(s) ofthe image stack, (ii) identifying the pixel set(s) as corresponding toat least a part of at least one droplet (which may comprise a part of asingle droplet, parts of multiple droplets, a whole droplet, a pluralityof whole droplets, or combinations thereof), (iii) identifyingindividual droplets from the pixel set or sets and (iv) determining thevolume of the identified droplet(s) based on the pixel set(s).

The sample may comprise a nucleotide. The sample may have beenamplified. The detectable agent may be fluorescent or luminescent. Theplurality of polydisperse droplets may comprise a first fluid and asecond fluid, the first fluid being immiscible with the second fluid.

The systems of the present disclosure further include a detection systemconfigured to analyze the volumes and the presence or absence of samplein the plurality of droplets. The detection systems can includedetectors for analyzing the contents of the volumes, determining volumesof droplets, and/or other characteristics of interest. The methodsdescribed herein will be generally compatible with any known systemscapable of detecting and analyzing volumes (e.g., droplets and/orwells).

In various aspects, the present disclosure provides systems and methodsfor performing digital measurements of samples. In certain aspects,droplets can be identified and their volumes measured using thepresently described systems and methods. In some aspects, the volume ofa droplet is measured by obtaining an image stack for a given droplet.Each image in the image stack corresponds to a measurement taken in asingle plane. Obtaining images for two or more planes in a given dropletenables the determination of droplet volume. If the droplet issufficiently small, it may be possible to determine its volume from itsappearance in a single image of the image stack. The image stack canalso be referred to as a “z-stack” since typically the focal planes areseparated by a user-chosen distance in the z-direction of themicroscope's optical system. The height of a given z-stack can be aslarge as the working distance of the microscope objective being used. Infurther aspects, the presence or absence of sample in a given dropletcan be determined for a given droplet. In certain aspects, the dropletvolume and determination of the presence or absence of sample in each ofa plurality of droplets can be used to determine the probability thatany given droplet in the plurality of polydisperse droplets wouldcontain sample, which can then be used to determine the concentration ofsample.

In various aspects, the present disclosure provides systems for usingdigital measurements to determine a concentration of a sample. Thesystems can include a sample holder containing a plurality ofpolydisperse droplets having a volume distribution; a detector fordetecting droplet size (i.e., volume) and a detectable agent containedin at least one droplet of the plurality of polydisperse droplets; and acomputer comprising a memory device with executable instructions storedthereon, the instructions, when executed by a processor, cause theprocessor to: analyze a plurality polydisperse droplets having a volumedistribution to determine the volumes of the droplets and whether theycontain a detectable agent to determine the concentration of the sample.In some aspects, the concentration of the detectable agent in the sampleis used to calculate the sample concentration. In various aspects, theconcentration of detectable agent is directly correlated with theconcentration of sample.

In various aspects, droplet diameter and the presence of a detectableagent is detected by an optical detection method. Any detector, orcomponent thereof, that operates by detecting a measureable opticalproperty, such as the presence of light, comprises an optical detector.Examples of optical detectors include, but are not limited to, cameras,photomultiplier tubes, photodiodes and photodiode arrays, andmicroscopes, and associated components thereof, such as objectives,optical filters, mirrors, and the like.

In certain aspects, the signal detected by an optical detector, or othersuitable detector, is processed in order to interpret the signals beingmeasured by the detector. In certain aspects, the measured informationis processed by a device, apparatus, or component thereof that storesand/or processes information acquired by a detector, such as, e.g., anoptical detector. Examples of an information processor include, but arenot limited to, a personal computing device that stores informationacquired by a detector, and software running on the personal computingdevice that processes the information. In other aspects, an informationprocessor or component thereof can be embedded in a detector, such as ina chip embedded in a camera that stores optical information acquired bythe camera either permanently or temporarily. In other aspects, aninformation processor and a detector can be components of a fullyintegrated device that both acquires and processes optical informationto perform a digital assay.

In yet another aspect, the systems can include a computer-readablestorage medium for conducting digital measurements. Thecomputer-readable storage medium has stored thereon instructions that,when executed by one or more processors of a computer, cause thecomputer to: analyze a plurality of droplets having a volumedistribution to determine a number of droplets in the plurality thatcontain the detectable agent; and use the number of droplets in theplurality of droplets, the volumes of some or all of the droplets in theplurality and the number of droplets in the second plurality containingone or more detectable agents to determine a concentration of thedetectable agent in the sample.

In another aspect, systems are provided for analyzing volumes to detectand calculate information for a given droplet. The system includes oneor more processors, and a memory device including instructionsexecutable by the one or more processors. When the instructions areexecuted by the one or more processors, the system at least receives auser input to analyze volumes (e.g., a plurality of droplets). Thesystem can be configured to carry out aspects of the methods of thepresent disclosure, such as counting a number of volumes (e.g.,droplets), determining volumes of a plurality of droplets in a volumedistribution and use the number of the droplets containing one or moredetectable agents to determine a concentration of the detectable agentin the sample. The system also provides data to a user. The dataprovided to the user can include the concentration of the detectableagent in the sample or a sample concentration.

In some aspects of the present disclosure, the presence of one or moretarget molecules within a droplet is indicated by an increase offluorescence in a particular wavelength range. In some aspects, a PCRreaction product indicates the presence of the target molecule by anincrease in the fluorescence in a particular wavelength range (indicatorfluorescence). In some aspects, a reference agent can be utilized inparallel with the target molecule. According to this aspect, thedroplets emit fluorescence (i.e., reference fluorescence) in awavelength range separate from that of the target molecule regardless ofwhether the target molecule is present. For a given set of droplets,separate sets of images of the indicator fluorescence and referencefluorescence are obtained and the droplets in each are identified andmeasured. The indicator and reference fluorescence from a given dropletcan be compared. In some aspects, the ratio of the indicator toreference fluorescence can be used to indicate whether that particulardroplet contains the target molecule. In other aspects, the absoluteintensity of the indicator fluorescence would be sufficient to indicateif the droplet contained target. In some aspects, the average value ofthe background pixels or a multiple thereof can be subtracted from thepixel intensities within the droplets before the fluorescenceintensities of the indicator and reference intensities are compared. Byperforming this analysis, a list of droplet diameters is obtained, andfor each measured droplet, a binary measure is obtained defining whetherthe droplet is occupied (contains one or more target molecules) or not.The list of droplet sizes and the total number of occupied droplets canthen be used to obtain the target concentration of the sample.

There are many possible ways to measure the size, contents, and/or otheraspects of polydisperse droplets in an emulsion while applying themethods of the present disclosure. In some aspects, droplets can bemeasured optically by an optical detector comprising a flow cytometer.According to this aspect, droplets can flow through a large flow channelwhere droplet shapes are not distorted and their volumes can bedetermined by computer software, based on measurements of lightscattering patterns acquired by an optical detector, such as aphotomultiplier tube, as the droplets pass a source of light excitation.In other aspects, droplets can pass through a narrow flow channel wherethe droplets conform to the channel width. According to this aspect, thevolume of the disperse droplets can be determined by using the channelwidth and the length of the individual droplets in the channel to definetheir volume.

A variety of signal detection methods can be used according to thepresent disclosure. In various aspects, the present methods and systemsprovide for detection of droplet aspects using optical detection methodsand optical detectors. In some aspects, the emulsion system can bemeasured optically by an optical detector comprising a fluorescencemicroscope and its associated components. Images can be acquired with,for example, a confocal laser scanning microscope, a spinning-disk(Nipkow disk) confocal microscope, or a microscope that usesprogrammable arrays of mirrors or spatial light modulators to acquiredata from multiple focal depths. In other aspects, images can beacquired with an epifluorescence microscope. In some aspects, imagesacquired with an epifluorescence microscope can be processedsubsequently using 3D deconvolution algorithms performed by computersoftware. In other aspects, images can be acquired with a multi-photonmicroscope, such a two-photon microscope. In other aspects images can beacquired using planar illumination microscopy, Bessel beam microscopy,differential interference contrast microscopy, phase contrastmicroscopy, bright field imaging, dark field imaging, or obliqueillumination. In some aspects, images can be acquired using acombination of the imaging devices and methods listed herein, or anyother suitable imaging devices and methods that can reasonably beapplied to the present methods.

The method of droplet imaging provides information on both the dropletsize and whether the droplet contains a target molecule of interest,which are used according to the present method for the determination ofsample concentration. In some aspects, droplet size and signal intensitycan be determined based on optical information acquired using confocalfluorescence microscopy. According to this aspect, the emulsion can bestored in a well, chamber, or other container and multiple sets of imagestacks can be acquired from it. In some aspects, for each sample area ina given polydisperse droplet sample, an image stack is collected,consisting of at least two images taken at approximately the sameXY-position (same sample area) but different Z-positions (differentdepths). Droplet(s) in the sample area that are larger than the spacingin Z will appear in multiple frames at approximately the same XYposition, but with different diameters. The image stack enables thedetermination of various parameters, including the droplet size and thepresence of absence of a target analyte in the droplet.

In some aspects, droplet diameters are determined by an informationprocessor based solely on droplets' boundaries determined in the frameof a Z-stack that contains the largest diameter. In other aspects,droplet diameters are determined by an information processor based ondroplet boundaries determined at multiple images in a Z stack, and therelative positions of the images in the Z dimension. This method caninclude an assumption of spherical droplet shape, or some other modifiedshape, depending on multiple factors including the refractive indices ofthe two fluids, the relative density of the two fluids and the surfacetension.

There are numerous methods to identify and select individual dropletsaccording to the present disclosure. In one aspect, line scans areobtained within the image and, after setting an appropriate thresholdlevel, the diameter of regions of interest are measured. In anotheraspect, a threshold for each image is chosen, and the areas above thethreshold are evaluated as possible single droplets. If the area issufficiently round (i.e., has an aspect ratio below a selected thresholdlevel), then the area is considered to be a single droplet. A list ofdroplets is generated for each image.

In some aspects, once droplets in an image have been identified, theyare correlated between different frames of the image stack. The largestdroplets will appear in more than one image so it is necessary toidentify the trail of circles through the frames of the image stack.Droplet correlation can be readily accomplished by using any number ofsuitable tracking algorithms as would be known to one of ordinary skillin the art. Tracking is generally facilitated by the fact that dropletsdo not move significantly between frames and because the droplets ofinterest are fairly large (in pixels). According to the presentdisclosure, the diameter of a particular droplet can be assumed to bethat of the largest circle associated with it in the image stack.Alternatively, a curve can be fit to the circle diameters of aparticular droplet and the largest diameter interpolated from thatcurve. That largest diameter would then be used as the diameter of thedroplet. In various aspects of the present disclosure, a plurality ofimages in the image stack are obtained and used to determine the variousparameters of interest for a given droplet, and the droplet itself isnot required to undergo additional assaying.

The present methods are amenable to automation and any suitable methodcan be used for the identification, selection, and analysis of dropletsand the samples contained within those droplets. Exemplary methodsinclude the Line Scan Method, Simple Boundary Method, Reverse Watershedmethod, Modified Reverse Watershed Method, Circle Detection Method,Circle Hough Transform Method, and Combined Reverse Watershed and CircleDetection Method. Other methods are also contemplated and within thescope of the present disclosure. Each of these methods is describedbelow.

Line Scan Method.

In one aspect of the present disclosure, the Line Scan Method can beused to analyze droplets in a polydisperse droplet system. According tothis aspect, line scans are obtained within the image and, after settingan appropriate signal threshold level, the diameter of regions ofinterest are measured.

Simple Boundary Method.

In one aspect of the present disclosure, the Simple Boundary Method canbe used to analyze droplets in a polydisperse droplet system. Accordingto this aspect, a threshold for each image is initially chosen. Pixelsets in a given sample that are above the threshold are evaluated aspossible single droplets. If the pixel set is sufficiently round (i.e.,has an aspect ratio below a chosen level) then the area is considered tobe a single droplet. A list of droplets is subsequently generated foreach image.

Reverse Watershed Method.

In one aspect of the present disclosure, the Reverse Watershed Methodcan be used to analyze droplets in a polydisperse droplet system. In thestandard watershed method, the pixel intensities of the image aretreated as elevations in a 3D topographical map. “Water” is introducedat the local minima where the height of the water relative to a globalzero point is the same for all “pools.” As the water height is raiseduniformly, the water in different pools will merge. The pixel locationsat which different pools merge is used to construct separate regionswithin the image.

In the Reverse Watershed Method, the pixels are treated the same, butthe “water” level is initially placed above the tallest “peaks” in theimage and then the water is drained, maintaining the same height ofwater throughout the image. As the water level falls, the most intensepixels will protrude above the water as small islands. These are notedas potential centroids of droplets and the size of each “island” istracked as the water level falls. This process continues until the waterlevel has fallen to a predetermined threshold. The islands are treatedas regions which can be all or part of a single droplet. Due tomeasurement noise, it is possible for a single droplet to have two ormore peaks within it having emerged during the above process. FIG. 1represents a typical image shown in gray scale. The Reverse WatershedMethod can be performed by any suitable means fitting within theseparameters. Example 3 below describes an exemplary set of steps by whichthe Reverse Watershed Method can be performed according to an aspect ofthe present disclosure.

According to some aspects of the present disclosure, the ReverseWatershed Method can be performed by first determining the standarddeviation of the signal within the background of each image andmultiplying it by a signal-to-noise-ratio (typically 2.5 to 3.5,however, the signal-to-noise ratio can be adjusted by the user dependingon the quantity of noise present in the images) and adding the result tothe average intensity of a background pixel. This process can proceediteratively and an initial estimate of the background cutoff is used toidentify probable background pixels (those pixels whose intensity isless than the initial estimate). The intensities of these pixels are inturn used to calculate the average and standard deviation of theintensity of the background pixels. The new average and standarddeviation are then used to estimate a new background cutoff. If the newbackground cutoff is significantly different from the original, then theprocess is repeated until the original background cutoff and the newbackground cutoff are in agreement.

Other methods for determining the background cutoff can also be used. Insome aspects the user can choose to define a cutoff to identifybackground pixels and forgo the iterative method described above. Insome aspects, the user can choose to identify certain pixels within theimage as background pixels and calculate the background and standarddeviation from those pixels. In other aspects, the user can calculatethe average and standard deviation of pixels in an image taken that hasno sample in it (i.e., a dark image). As described below, the averagevalue of the background pixels can be used in analyzing the fluorescenceto determine which droplets contain the target molecule.

According to some aspects of the present disclosure, a cutoff thresholdis then selected. The cutoff threshold is typically selected at ornearly at the largest pixel intensity of the image. This cutoffthreshold is lowered in steps until it reaches a smallest cutoffthreshold (SCT). In some aspects, the SCT is equivalent to thebackground threshold (BT). In other aspects, the SCT can be a differentvalue calculated from the average and standard deviation of thebackground pixel intensities. In other aspects, the SCT can be auser-defined value. Once the SCT is determined, the user selects thenumber of steps and the spacing between successive cutoff thresholds.The SCT is chosen to identify pixels that are part of droplets. The BTis chosen to identify pixels that are part of the background. In someaspects the BT can be less than the SCT, in which case, there can besome pixels that are not assigned to either a droplet or the background.

According to some aspects of the present disclosure, imaging analysissoftware can then be used at each step to find sets of connected pixels(hereafter referred to simply as a “pixel set”) in the image above thecurrent step's cutoff threshold. In some aspects the user can requirethe set of pixels to be either 4-connected or 8-connected. A set ofpixels in a square array are considered “4-connected” if each pixel ishorizontally or vertically adjacent to at least one other pixel in theset. A set of pixels in a square array are considered “8-connected” ifeach pixel is horizontally, vertically or diagonally adjacent to atleast one other pixel in the set. In some aspects, a different form ofconnectivity can be used to define connected sets of pixels in theimage. In some aspects, a user-defined structuring element can be usedto morphologically close the connected sets of pixels determined by thecutoff. If the area of such a pixel set exceeds a user-defined criterion(i.e., a “minimum required area,” or “MRA”), then it is marked as aregion of interest (ROI). By using a MRA before a given pixel set isaccepted as a ROI, it is possible to discriminate against noise in thebackground pixels. Noise can cause isolated pixels in the background tohave an intensity that is larger than a desired SCT. The user-definedMRA can be used to exclude such isolated pixels. The MRA is chosen suchthat the probability that a given set of connected background pixelshaving an area larger than the MRA can all have intensities larger thanthe SCT is small enough that the user is satisfied that the objectsfound are in fact droplets and not noise in the background. The size ofthe MRA can be chosen based on the quantity of noise within the dropletarea and the area of the smallest droplet in the image that the userwishes to be able to identify.

Once a ROI appears in a particular location of the image, its area canbe tracked as the cutoff threshold is decreased. The location of themaximum intensity pixel within each ROI and the values of the pixelswithin the ROI can also be tracked. The pixel sets that are identifiedwith the SCT are referred to as “Groups.” If a Group contains more thanone droplet, regions of pixels inside the Group can actually representspace between the droplets. If three or more droplets are contained in asingle Group, it is possible that there could be gaps between thedroplets that would appear as holes in the interior of the Group. Insome aspects a hole-threshold (HT) to identify holes is applied to findpossible holes composed of connected pixels inside a single Group. Auser-specified minimum size for holes is specified to distinguish holesfrom noise in the image. Only sets of connected pixels whose areas equalor exceed the minimum size for holes would be marked as holes. In someaspects the HT would equal the SCT. In other aspects, the user canchoose a HT which was not equal to the SCT.

The external boundary of a Group is composed of pixels within the groupthat are adjacent to a pixel that is outside the Group with intensitybelow the SCT and/or in the Group's interior and adjacent to a pixel ina hole. These pixels are referred to as non-group pixels. The ReverseWatershed procedure then identifies external boundary pixels that arepart of the same droplet and a best-fit circle to those externalboundary pixels is determined using existing optimization methods.

According to some aspects of the present disclosure, as the cutoffthreshold is lowered, two or more ROIs can merge. A pixel set that isabove a particular cutoff threshold level can include two or more ROIsthat were separate for a larger cutoff threshold. This can happenbecause either the different ROIs represent different droplets that areso close together that the boundary region between them has a largerpixel intensity than the current cutoff threshold, or the amplitude ofnoise in the sample is sufficiently large that two or more regionswithin a single droplet exhibit local maxima. These maxima can appear tothe algorithm as separate ROIs at larger cutoff thresholds.

According to further aspects of the present disclosure, a user-definedcriteria can be used to decide if different ROIs whose areas arecontained within the same pixel set of the current step should (a) bemerged and thereafter be treated as one ROI or (b) not be merged andtracked as separate ROIs. These criteria can include, withoutlimitation: (i) the distance between the maximum intensity pixels of thedifferent ROIs, and/or (ii) the values of the maximum intensity pixelsof the different ROIs as compared to the smallest intensity pixels thatseparate them in the pixel set, and/or (iii) the values of the maximumintensity pixels after smoothing of the different ROIs.

For criterion (i) above, a smoothed version of the image can be usedinstead of the actual image. Smoothing the image can reduce theinfluence of noise in assessing the distance between the “peaks” of thetwo ROIs. Additionally, for criterion (i) above, the centroids oranother estimator of center of the ROI can also be used. Examples ofthis include an unweighted centroid where each pixel contributes equalweight to determining the centroid or a weighted centroid where eachpixel contributes a weight equal to some function of its intensity tothe centroid.

For criterion (ii) above, if the ROIs are parts of separate droplets, itwould be expected that they would be separated by a region of pixelsthat are significantly smaller in intensity than the peaks of the twoROIs. If instead the intensities of the pixels that lay between the twopeaks are similar to the intensity of the peaks, then it can beconcluded that the two ROIs are in fact part of the same droplet andshould be combined. The user-defined criteria can be based on a functionthat depends on any property of the image that can include: (a) themaximum peak intensity of the ROI, (b) the maximum peak intensity of theROI after smoothing, (c) the average background intensity, (d) thestandard deviation of the background intensities, (e) the cutoff levelused to determine the current pixel set or (0 any arbitraryuser-specified value.

For criterion (iii) above, in some aspects noise in the image can resultin a single pixel containing the maximum intensity of the ROI surroundedby pixels of much smaller intensities. This can be revealed in somecases by smoothing because the maximum pixel intensity of the ROI aftersmoothing would be significantly lower. If such smoothing reduces themaximum intensities of the two ROIs below a user-defined level, then thetwo ROIs would be determined to be part of the same droplet andcombined. The user-defined level can be a function that depends on anyproperty of the image that can include: (a) the maximum peak intensityof the ROI, (b) the maximum peak intensity of the ROI after smoothing,(c) the average background intensity, (d) the standard deviation of thebackground intensities, (e) the cutoff level used to determine thecurrent pixel set or (0 any arbitrary user-specified value.

According to certain aspects of the present disclosure, if differentROIs whose areas are contained within the same pixel set of the currentstep are not merged, then the pixels of that pixel set that were notpreviously assigned to a ROI must be assigned by one of a few methods,such as the following two possible methods. First, a list of unassignedpixels within the pixel set is sorted by intensity, and the pixel withthe largest intensity that is immediately adjacent to one and only oneof the ROIs is assigned to that ROI. This process is repeated until theonly unassigned pixels remaining are those that are immediately adjacentto two or more different ROIs, in which case, those pixels remainunassigned. Second, the unassigned pixels can be left unassigned untilafter the last step (i.e., the SCT has been used and the pixel set isthen referred to as a Group). In that case, the first method describedin this paragraph above is then applied to all the unassigned pixels ofthe Group.

According to certain aspects of the present disclosure, the result ofthe procedure to this point can be applied to a droplet image. Accordingto this aspect, the droplet image can be divided into Groups that areseparated by pixels whose intensity is below the SCT. Some of the Groupscontain only a single ROI and some contain two or more ROIs. Theboundary pixels are those pixels belonging to a Group that are adjacentto a non-group pixel.

According to certain aspects of the present disclosure, if a Groupconsists of only a single ROI, then it is considered to be a singledroplet and its boundary pixels are fit to a circle to obtain a dropletdiameter.

According to further aspects of the present disclosure, if a Groupconsists of two or more ROIs, then sets of ROIs (i.e., sets comprisingone or more ROIs) from that group are analyzed. The boundary pixels thatare part of the set being analyzed are fit to a circle. User-definedcriteria are then applied to the best-fit circle to determine whetherthe ROIs of the set should be combined and considered to be part of asingle droplet. This procedure can be applied iteratively, piecingtogether a droplet one ROI at a time. Possible criteria that can be usedto decide which combinations of ROIs to check include, but are notlimited to: (i) checking pairs of ROIs that are adjacent to each other(their internal boundaries within the Group are near each other); (ii)checking pairs of ROIs whose best-fit circles have centers that areclose to each other; and (iii) checking ROIs whose areas liesubstantially inside the best-fit circle of another ROI or set of ROIs.Possible criteria that can be used to determine if two or more ROIsshould be combined and classified as a single droplet include, but arenot limited to: (i) the quality of the fit (as defined by mean squarederror or some other statistical measure of the goodness of a given fit);(ii) how much of the area of the ROIs from the set lie within thebest-fit circle; (iii) how much of the area within the best-fit circleconsists of pixels in the image background; and (iv) the circularity ofthe boundary pixels included in the fit.

In another aspect, the above protocol can include additionalmodifications. Possible modifications to this procedure can includeexamining the boundary pixels of a Group and not including in any fitthose pixels that appear to be noise. An example of a criterion that canbe used is that any boundary pixel that is not adjacent to an interiorpixel of the Group would not be included in any fit of the boundary to acircle. In this example an interior pixel can be a pixel that is amember of the Group, but that is not a boundary pixel, i.e., is notadjacent to a non-group pixel.

Another possible modification to the above-described Reverse WatershedMethod can be that the BT and SCT can be different. A backgroundthreshold that is less than the smallest cutoff threshold can be used toeliminate from the set of background pixels those areas that containobjects too faint to be characterized. These areas can contain signalfrom different focal planes of droplets either above or below the focalplane of the sample being analyzed. A typical example of this occurswhen the sample is imaged with fluorescence microscopy. Due to thelimitations of the microscope's resolution in the z-direction,fluorescence from one focal plane can bleed through into images of otherfocal planes.

Other modifications to the Reverse Watershed Method described above arepossible according to the present disclosure. Possible modifications tothis procedure can include examining the boundary pixels of a Group andnot including in any fit those pixels that appear to be noise. Anexample of a criterion that can be used is, for example, adopting apresumption that any boundary pixel that is not adjacent to an interiorpixel of the group would not be included in any fit of the boundary to acircle. According to this assumption, an interior pixel can be a pixelthat is a member of the Group, but that is not a boundary pixel, i.e.,is not adjacent to a non-group pixel.

In certain aspects, the Reverse Watershed Method can be modified suchthat the BT and SCT are permitted to be different. A BT that is lessthan the SCT can be used to eliminate from the set of background pixelsthose areas that contain objects that are too faint to be characterized.These areas can contain signal from different focal planes of dropletseither above or below the focal plane of the sample being analyzed. Atypical example of this occurs when the sample is imaged withfluorescence microscopy. Due to the limitations of the microscope'sresolution in the z-direction, fluorescence from one focal plane canbleed through into images of other focal planes.

Circle Detection Method. In one aspect of the present disclosure, theCircle Detection Method can be used to analyze droplets in apolydisperse droplet system. According to this method, a threshold(determined as for the Reverse Watershed Method above) is applied to theimage. As described in the Reverse Watershed Method, the SCT can be usedto identify Groups, however, ROIs are not identified. The hole-thresholdcan also be applied to identify holes within single Groups as describedin the Reverse Watershed Method. After identifying the hole-threshold,the external boundary of each Group can be determined as described inthe Reverse Watershed Method. In some aspects, the boundaries of theGroups formed can then be analyzed by the Circle Hough Transform. TheCircle Hough Transform is a generalization of the original HoughTransform (i.e., as used to detect lines in images) to detect shapes forwhich an analytical description exists (in this case circles). Accordingto certain aspects of the present disclosure, the Circle DetectionMethod analyzes the coordinates of the external boundary pixels (alsoknown as “feature pixels”) to find sets of boundary pixels that form allor part of a circle. Identification of the boundary pixels results in alarge number of potential circles that are analyzed and only the oneslikely to be droplets are retained.

According to this method, circles identified by the Circle DetectionMethod can be superimposed upon an image, such as is described inExample 5 below. Regions not meeting the criteria set forth in theCircle Detection Method can be discarded. For instance, a circle formedfrom some or the entire external boundary of one Group cannot includepixels from a different, separate Group. Possible criteria that can thenbe applied according to this method can include, but are not limited to:(i) selecting potential circles that overlap or lie adjacent to a maximpossible percentage of the group's boundary pixels; (ii) selectingpotential circles for which the fraction of its circumference pixelsthat overlap or lie adjacent to a boundary pixel is as close to one aspossible; (iii) rejecting potential circles that have significant amountof their circumference entirely within a group; (iv) rejecting potentialcircles whose areas include a significant number of non-group pixels;(v) rejecting potential circles whose areas include pixels in adifferent Group; (vi) for a particular Group, rejecting potentialcircles whose areas include a significant number of pixels in a hole ofthat Group; and/or (vii) rejecting potential circles if the best-fitcircle for given feature pixels are judged to be of a low quality (i.e.,wherein the degree of quality is a user-defined measure of the goodnessof a given fit that is statistically calculated and a low quality fit isone in which the fit failed a user-defined criteria).

In certain aspects, there may be overlapping circles at this point. Suchpairs would be examined to determine if either should be rejected.Criteria that can be applied to such pairs include, but are not limitedto: (i) if the amount of unique area in one of the circles (i.e., thearea in one circle that is not in the other) is less than a user-definedfraction of the total area, then one of the circles is removed and (ii)if the number of unique feature pixels (i.e., feature pixels for onecircle that are not feature pixels for the other) is less than auser-defined fraction of the total number of feature pixels, then one ofthe circles is removed. If one circle of a pair is to be removed, thenpossible criteria used to determine which circle will be removed caninclude, but are not limited to: (i) removing the circle with thesmaller number of feature pixels; (ii) removing the circle with thesmallest area; or (iii) removing the circle that contains the largernumber of pixels that are not part of the Group (i.e., the largestnumber that are in the background) or that has the larger fraction ofits area not included as part of the Group.

After applying the above criteria, there can still be circles thatoverlap with each other significantly. Deciding whether to accept suchcircles as droplets would depend on the nature of the emulsion. In someemulsion systems, it can be common to find droplets pushed together insuch a way as to flatten the surfaces in contact, which can have theeffect of distorting the droplets (i.e., causing them to take a shapeother than strictly spherical). In this instance, the user can decidewhether to include or exclude those droplets, depending on therequirements for accuracy in the determination of the size of suchdroplets. In some systems, small droplets can overlap with much largerdroplets. In that case, the circles that describe the smaller dropletscan have a significant fraction of their area inside a much largercircle. If enough of the small droplet's boundary is part of its Group'sexternal boundary, the user can choose to accept the small droplet andinclude it in the analysis. In some aspects, circles can have asignificant fraction of their circumference in the interior of a Group.In certain aspects, a user-defined criteria can be used to excludedroplets with more than a specified fraction circles of their boundaryin the interior of the Group on the grounds that the circle is anartifact due to noise in the image distorting the exterior boundary ofthe Group. In some aspects, two possible droplets of similar size have asignificant amount of overlap. This can be due to a distortion due todroplets being pushed together as noted above. Or, this can be due to anoptical distortion that results in a spherical droplet assuming anelliptical shape in the image. User criteria can be used to mark suchcircles and exclude them from further analysis.

In some aspects, the user can apply a quality-of-fit test to thedroplets and reject those that are deemed not accurately sized. Agoodness-of-fit statistic can be calculated for the best fit of a circleto the feature pixels of a droplet and the droplet can be rejected if itfailed to meet a user-defined standard. In other aspects, the intensitywithin the droplet can be examined and the droplet can be rejected if bysome measure the overall droplet intensity is too low. One way this canoccur is due to the limited resolution of the microscope in thez-direction. Fluorescence from droplets at one position in thez-direction can show up at greatly reduced intensity in images of thesample taken for a different position in the z-direction. A test ofoverall intensity can be used to identify and reject such faint objects.

In another aspect, the above protocol can include additionalmodifications. Possible modifications to this procedure can includeexamining the boundary pixels of a Group and not including in any fitthose pixels that appear to be noise. An example of a criterion that canbe used is that any boundary pixel that is not adjacent to an interiorpixel of the Group would not be included in any fit of the boundary to acircle. In this example, an interior pixel can be a pixel that is amember of the Group, but which is not a boundary pixel, i.e., is notadjacent to a non-group pixel.

Another possible modification to the above-described Circle DetectionMethod can be that the BT and SCT can be different. A BT that is lessthan the SCT can be used to eliminate from the set of background pixelsthose areas that contain objects too faint to be characterized. Theseareas can contain signal from different focal planes of droplets eitherabove or below the focal plane of the sample being analyzed. A typicalexample of this occurs when the sample is imaged with fluorescencemicroscopy. Due to the limitations of the microscope's resolution in thez-direction, fluorescence from one focal plane can bleed through intoimages of other focal planes.

Other modifications to the Circle Detection Method described above arepossible according to the present disclosure. Possible modifications tothis procedure can include examining the boundary pixels of a Group andnot including in any fit those pixels that appear to be noise. Anexample of a criterion that can be used is, for example, adopting apresumption that any boundary pixel that is not adjacent to an interiorpixel of the Group would not be included in any fit of the boundary to acircle. According to this assumption, an interior pixel can be a pixelthat is a member of the Group, but which is not a boundary pixel, i.e.,is not adjacent to non-group pixel.

Another possible modification to the Circle Detection Method is that theBT and SCT are permitted to be different. A BT that is less than the SCTcan be used to eliminate from the set of background pixels those areasthat contain objects that are too faint to be characterized. These areascan contain signal from different focal planes of droplets either aboveor below the focal plane of the sample being analyzed. A typical exampleof this occurs when the sample is imaged with fluorescence microscopy.Due to the limitations of the microscope's resolution in thez-direction, fluorescence from one focal plane can bleed through intoimages of other focal planes.

After sorting the circles, the ones that best define the droplets areused to find which boundary pixels should be used to describe thedroplet. These pixels are then fit to a circle to obtain a collection ofbest-fit circles corresponding to droplets.

In other aspects, the Circle Hough Transform Method can be replaced by adifferent feature extraction method that would be used to detectcircular objects by analyzing the boundary pixels in the image.

Combined Reverse Watershed and Circle Detection Method. In yet anotheraspect of the present disclosure, aspects of the Reverse Watershed andCircle Detection Methods are combined to yield the Combined ReverseWatershed and Circle Detection Method for the analysis of droplets in apolydisperse droplet system. According to this method, the ROIs and theboundary pixels of Groups (i.e., pixel sets found for the SCT) aredetermined using the procedure described in the Reverse WatershedMethod. Then for each ROI, the Circle Hough Transform is applied to theexternal boundary pixels of the ROI that are also external boundarypixels of the Group that contains the ROI. The circles for a particularROI are sorted according to user-determined criteria to find thesmallest number of circles that describe the boundary of that ROI. Inmost cases there will be one circle per ROI. Possible criteria that canbe used include, but are not limited to: (i) selecting circles thatinclude the largest fraction of the ROI's external boundary pixels; (ii)selecting circles that include the largest fraction of the ROI's area;(iii) rejecting circles that include pixels from a different Group; (iv)rejecting circles that include a substantial number of non-group pixels;(v) discriminating against circles that have a substantial fraction oftheir circumference in the interior of the Group.

According to certain aspects of the present disclosure, the initial setof circles for a ROI can be examined in pairs, with one of the twocircles being rejected in favor of the other. Possible criteria that canbe used here include, but are not limited to: (i) if the centers of twocircles of the same or similar size are in close proximity to oneanother, then rejecting the circle with the smaller number of votes or(ii) if two circles have more than a user-defined fraction of theirvotes in common, then rejecting the circle with the smaller number ofvotes. For example if a possible Hough Transform circle includesexternal boundary pixels from a particular ROI, then the circle would berejected unless it encompassed at least some user-defined fraction ofthat ROI's area. In this case, the minimum required fraction can dependon how many boundary pixels of the ROI are associated with the HoughTransform circle.

Also, in cases where there are multiple droplets in close proximity toone another, the intensities of pixels that are close to two or moredroplets, but not actually part of any of the droplets, can have anelevated intensity relative to the background and can be included aspart of the Group and form part of the external Group boundary. In theReverse Watershed method, this can lead to difficulties, since theadditional pixels included in the Group will cause portions of theexternal boundary to be non-circular. The inclusion of external boundarypixels that are not actually part of the droplet can result in abest-fit circle that is a less accurate description of the droplet. Theproblem of the region between two droplets having elevated pixelintensities leading to a non-circular boundary can be mitigated by theuse of the Circle Hough Transform, since it discriminates againstincluding pixels in the fit that would form a non-circular boundary.

The circle or circles associated with an ROI are estimates of the sizeof the droplet the ROI can be a part of. This information is used togroup the ROIs into droplets. For example, if the circles associatedwith two ROIs in the same Group have similar radii and have centers thatare close together, then the two ROIs will be considered to be part ofthe same droplet. User-defined criteria would be used to decide howsimilar the radii of the circles must be and how close the centers ofthe circles must be in order for the two ROIs to be combined into onedroplet. The criterion relating to how close the centers must be candepend on the size of the two circles.

It is possible that an ROI can be assigned to two or more droplets, orconsidered for assignment to two or more droplets. In some aspects,possible criteria to determine which droplet the ROI should be assignedto include, but is not limited to: (i) calculating a goodness of fitstatistic to the feature pixels of just the ROI being considered usingthe parameters the best-fit circle for each of the droplets andassigning the ROI to the droplet whose circle is the best fit to thefeature pixels of the ROI or (ii) assigning the ROI to the droplet withwhich it has the largest overlap in area.

In some aspects, after all the ROIs with circles are assigned todroplets, any remaining external boundary pixels that are not part ofany circle are checked to see if they lie within a user-defined distanceof the boundary of an existing circle. If so those external boundarypixels are included in the boundary of the droplet. Unassigned externalboundary pixels that still lie on a droplet's boundary can occur if theexternal boundary of a ROI is distorted by noise such that the CircleHough Transform finds no acceptable circles for that ROI. Then theexternal boundary pixels for each droplet are fit to a circle to obtaina size and a position. Droplets that overlap significantly can beaccepted or discarded depending on user-defined criteria for the amountof such overlap that is allowed and that can depend on the properties ofthe emulsion. Droplets that appear to have a significant fraction of itsboundary in the interior of a group can be accepted or discardeddepending on user-defined criteria. In addition, if the user is willingto accept slightly distorted droplets, the Hough Transform can be usedto detect ellipses in the image, and those ellipses that satisfy auser-set criterion (such as having an aspect ratio less than a userselected limit) can be accepted as droplets.

This method can include additional modifications. Possible modificationsto this procedure can include examining the boundary pixels of a Groupand not including in any fit those pixels that appear to be noise. Anexample of a criterion that can be used is that any boundary pixel thatis not adjacent to an interior pixel of the Group would not be includedin any fit of the boundary to a circle. In this example an interiorpixel can be a pixel that is a member of the Group, but which is not aboundary pixel, i.e., is not adjacent to a non-group pixel.

Another possible modification to the above-described Combined ReverseWatershed and Circle Detection Method can be that the BT and SCT can bedifferent. A BT that is less than the SCT can be used to eliminate fromthe set of background pixels those areas that contain objects too faintto be identified. These areas can contain signal from different focalplanes of droplets either above or below the focal plane of the samplebeing analyzed. A typical example of this occurs when the sample isimaged with fluorescence microscopy. Due to the limitations of themicroscope's resolution in the z-direction, fluorescence from one focalplane can bleed through into images of other focal planes.

Other modifications to the Combined Reverse Watershed and CircleDetection Method described above are possible according to the presentdisclosure. Possible modifications to this procedure can includeexamining the boundary pixels of a Group and not including in any fitthose pixels that appear to be noise. An example of a criterion that canbe used is, for example, adopting a presumption that any boundary pixelthat is not adjacent to an interior pixel of the Group would not beincluded in any fit of the boundary to a circle. According to thisassumption, an interior pixel can be a pixel that is a member of theGroup, but which is not a boundary pixel, i.e., is not adjacent to anon-group pixel.

Another possible modification is that the BT and SCT are permitted to bedifferent. A BT that is less than the SCT can be used to eliminate fromthe set of background pixels those areas that contain objects that aretoo faint to be characterized. These areas can contain signal fromdifferent focal planes of droplets either above or below the focal planeof the sample being analyzed. A typical example of this occurs when thesample is imaged with fluorescence microscopy. Due to the limitations ofthe microscope's resolution in the z-direction, fluorescence from onefocal plane can bleed through into images of other focal planes.

In another aspect, the Circle Hough Transform can be replaced by adifferent feature extraction method that identifies circles. In thatcase the information produced by the alternate feature extraction methodwould be used to identify droplets.

In yet another aspect, this method can be used to search fornon-circular objects in an image. The Circle Hough Transform would bereplaced by a feature extraction method that identifies objects of thedesired shape.

Determination of Occupancy. In some aspects, after the droplets havebeen identified and their size determined, the fluorescence intensity isused to determine if the droplet contained the target molecule.

In some aspects, the presence of the target molecule would result in anincrease of the fluorescence from the droplet. In those cases, anintensity cutoff standard can be imposed wherein a droplet whoseintensity exceeds the cutoff is considered to be occupied and theremainder would be considered empty. In systems where the presence ofthe target molecule results in a decrease of fluorescence, dropletswhose intensities exceed the cutoff are considered to be empty and theothers would be considered occupied. In both cases, the intensity of adroplet being compared to the cutoff can be: (i) the average intensitywithin the droplet; (ii) the peak intensity within the droplet or (iii)any user-chosen function of the intensities of the pixels within thedroplet (for example the median intensity or a percentile of theintensities can be used).

In some aspects the method for determining occupancy would use twofluorescence images of each droplet. In one of the images the intensityof the fluorescence would depend measurably on whether the droplet wasoccupied. In the other image, the intensity of the fluorescence would beunchanged or little changed by the presence of the target molecule. Afunction of the intensities of the droplet from the two images such asthe ratio can be used to decide the occupancy of the droplet. Using aratio or some other function instead of the intensity from a singleimage can correct for the possible instrumental artifacts. Furthermore,for larger droplets, fluorescence from focal planes in the sample abovethe plane being imaged can appear in the image causing an increase inthe measured intensities of the pixels within that droplet. Using theintensities of a droplet from two different images would allow the userto avoid these problems. The intensities of a droplet being analyzed canbe: (i) the average intensity within the droplet; (ii) the peakintensity within the droplet or (iii) any user-chosen function of theintensities of the pixels within the droplet (for example the medianintensity or a percentile of the intensities can be used). Theintensities can, at the user's discretion, be background subtracted. Insome aspects, the average background used to identify the Groups issubtracted from the intensity of each pixel in the image.

In some aspects, a corrected set of background pixels is determined atthis stage. One method for determining the corrected set is to startwith the set of pixels that are inside the Groups (that may includepixels in holes interior to the Groups). At the user's discretion, thesesets of pixels can be dilated (i.e., enlarged) by one or more pixels.The pixels that were not included in these sets of pixels would form theset of corrected background pixels.

Exemplary Analysis System and Methods. As discussed herein, the presentdisclosure includes detection systems configured to analyze the volumesand the presence or absence of sample in the plurality of droplets of anemulsion system. FIG. 2A schematically illustrates an exemplarydetection system 1000. The detection system may comprise a computingdevice 1001 configured to be operated by a user US, an imaging source1040 configured to be operated by the computing device 1001, and amulti-well plate 1050 configured to be imaged by the imaging platform orsource 1040 and which may contain a droplet system or emulsion system1055 to be imaged and analyzed.

The computing device 1001 may be programmed to implement one or more ofthe methods described herein. The computing device 1001 may comprise apersonal computer, a workstation, or a server, for example. Thecomputing device 1001 includes a processor, computer processor, centralprocessing unit, or CPU 1005, which can be a single core or multi-coreprocessor, or a plurality of processors for parallel processing.

The computing device 1001 may also include a memory 1010 (e.g.,random-access memory, read-only memory, flash memory, a hard disk, orthe like). The memory 1010 can store files, such as computer readableimage files taken by the imaging source 1040. The computing device 1001in some cases can include one or more additional data storage units thatare external to the computing device 1001, such as located on a remoteserver that is in communication with the computing device 1001 throughthe one or more networks.

The computing device 1001 may further comprise an input/output or I/Osystem 1015 which can be used by the computing device 1001 tocommunicate with one or more of the user US, one or more other computingdevices or systems, one or more networks (e.g., a local area network(LAN), an extranet, an intranet, the Internet, a telecommunicationsnetwork, a data network, a cellular data network, or the like), or oneor more peripheral devices including the imaging source 1040, externalmemory, various adapters, etc. The I/O system 1015 may comprise adisplay 1020, a user interface 1025, and a communications interface1030. The display 1020 may comprise a touch screen display through whichthe user interface 1025 is projected to the user US, for example. Thecommunications interface 1030 may comprise a network adaptor for thecomputing device 1001 to connect to the one or more networks. The userUS, for example, may operate the computing device 1001 through the oneor more networks remotely. For instance, the computing device 1001 maycomprise a computing system based in the cloud such a distributedcomputing system which operates the imaging source 1040 which may belocal to the user US. The computing device 1001 can be in communicationwith the imaging source 1040 through the one or more networks or bydirect communication.

Methods as described herein can be implemented by way of machine (orcomputer processor) executable code (or software) stored on anelectronic storage location of the computing device 1001, such as, forexample, on the memory 1010 or other electronic storage unit. Duringuse, the code can be executed by the processor 1005. In some cases, thecode can be retrieved from the storage unit and stored on the memory1010 for ready access by the processor 1005. In some situations, theelectronic storage unit can be precluded, and machine-executableinstructions are stored on memory 1010. Alternatively, the code can beexecuted on a remote computer system. The code executed may operate theimaging source 1040 to image and analyze the multi-well plate 1050 inaccordance with any of the methods described herein. The code may beexecuted automatically by the computing device 1001 or may be executedin accordance with instructions provided by an operator such as the userUS.

The code can be pre-compiled and configured for use with a machine havea processer adapted to execute the code, or can be compiled duringruntime. The code can be supplied in a programming language that can beselected to enable the code to execute in a pre-compiled or as-compiledfashion.

Aspects of the systems and methods provided herein, such as thecomputing device 1001, can be embodied in programming. Various aspectsof the technology may be thought of as “products” or “articles ofmanufacture” typically in the form of machine (or processor) executablecode and/or associated data that is carried on or embodied in a type ofmachine readable medium. Machine-executable code can be stored on anelectronic storage unit, such memory (e.g., read-only memory,random-access memory, flash memory) or a hard disk. “Storage” type mediacan include any or all of the tangible memory of the computers,processors or the like, or associated modules thereof, such as varioussemiconductor memories, tape drives, disk drives and the like, which mayprovide non-transitory storage at any time for the software programming.All or portions of the software may at times be communicated through theInternet or various other telecommunication networks. Suchcommunications, for example, may enable loading of the software from onecomputer or processor into another, for example, from a managementserver or host computer into the computer platform of an applicationserver. Thus, another type of media that may bear the software elementsincludes optical, electrical and electromagnetic waves, such as usedacross physical interfaces between local devices, through wired andoptical landline networks and over various air-links. The physicalelements that carry such waves, such as wired or wireless links, opticallinks or the like, also may be considered as media bearing the software.As used herein, unless restricted to non-transitory, tangible “storage”media, terms such as computer or machine “readable medium” refer to anymedium that participates in providing instructions to a processor forexecution.

Hence, a machine readable medium, such as computer-executable code, maytake many forms, including but not limited to, a tangible storagemedium, a carrier wave medium or physical transmission medium.Non-volatile storage media include, for example, optical or magneticdisks, such as any of the storage devices in any computer(s) or thelike, such as may be used to implement the databases, etc. shown in thedrawings. Volatile storage media include dynamic memory, such as mainmemory of such a computer platform. Tangible transmission media includecoaxial cables; copper wire and fiber optics, including the wires thatcomprise a bus within a computer system. Carrier-wave transmission mediamay take the form of electric or electromagnetic signals, or acoustic orlight waves such as those generated during radio frequency (RF) andinfrared (IR) data communications. Common forms of computer-readablemedia therefore include for example: a floppy disk, a flexible disk,hard disk, magnetic tape, any other magnetic medium, a CD-ROM, DVD orDVD-ROM, any other optical medium, punch cards paper tape, any otherphysical storage medium with patterns of holes, a RAM, a ROM, a PROM andEPROM, a FLASH-EPROM, any other memory chip or cartridge, a carrier wavetransporting data or instructions, cables or links transporting such acarrier wave, or any other medium from which a computer may readprogramming code and/or data. Many of these forms of computer readablemedia may be involved in carrying one or more sequences of one or moreinstructions to a processor for execution.

The results of methods of the disclosure can be displayed to a user onthe user interface or UI 1025 or other user interface, which may includea graphical user interface (GUI), of an electronic device of the user USor other operator. The other UI, such as GUI, can be provided on adisplay of an electronic device of the user such as a tablet computer, asmartphone, a wearable computer, or the like. The display can be acapacitive or resistive touch display, for example. Such displays can beused with other systems and methods of the disclosure.

The imaging source 1040 may comprise any of the imaging devices andsources described herein. The imaging source 1040 may comprise, forexample, an optical imaging source. The imaging source 1040 may beconfigured to perform one or more of confocal microscopy, line confocalmicroscopy, deconvolution microscopy, spinning disk microscopy,multi-photon microscopy, planar illumination microscopy, Bessel beammicroscopy, differential interference contrast microscopy, phasecontrast microscopy, epiflouorescent microscopy, bright field imaging,dark field imaging, oblique illumination, or a combination thereof.

The multi-well plate 1050 may comprise any multi-well plate known in theart. The droplet system or emulsion system 1055 may be generated by anyof the methods described herein.

The exemplary detection system 1000 may be operated by the user US toimplement any of the methods described herein. For example, thedetection system 1000 may be operated by the user US to implement anexemplary detection method 1100 schematically illustrated in FIG. 2B oran exemplary detection method 100 schematically illustrated in FIG. 2C.The detection method 1100 of FIG. 2B may comprise various steps asfollows. In a step 1110, a droplet or emulsion system may be generated.The droplet or emulsion system may be generated in the many ways asdescribed herein such as by shaking, vortexing, or other agitation. In astep 1120, the droplet or emulsion system may be provided on amulti-well plate in many ways as described herein. In a step 1130, animage stack of the droplet or emulsion system may be generated in themany ways as described herein. In a step 1140, the image stack may beanalyzed to detect or recognize droplets in the many ways as describedherein. For example, one or more of the Line Scan Method, the SimpleBoundary Method, the Reverse Watershed Method, the Circle DetectionMethod, the Combined Reverse Watershed and Circle Detection Method, orcombinations thereof may be used to detect or recognize the droplets. Ina step 1150, the presence of sample may be detected in the variousdroplets (i.e., occupancy may be determined) in the many ways asdescribed herein. In a step 1170, the concentration of the sample may bedetermined based on the detected presence of the sample in the variousdroplets and the size distribution of the various droplets in the manyways as described herein (e.g., with the statistical methods describedherein).

The detection method 100 of FIG. 2C may comprise various steps asfollows. In a step 105, a sample may be obtained. The sample may beobtained in any of the ways described herein. In a step 110, an emulsionis prepared from the sample. The emulsion may be prepared in any of theways described herein. In a step 115, the target may be amplified. Thetarget may be amplified in any of the ways described herein. In a step120, the emulsion is placed in a well or chamber. In some embodiments,the steps 110 and 120 may occur concurrently and the emulsion may beprepared in the well or chamber. In a step 125, the emulsion may beimaged at a first horizontal location and a first vertical location. Ina step 130, the emulsion may be imaged at the same, first horizontallocation and a second vertical location different from the firstvertical location. In a step 135, the imaging steps may be repeated for2+n vertical locations. In a step 140, a plurality of images may beacquired such as by performing the previous steps 125, 130, and 135. Ina step 145, the acquired images are analyzed for droplet sizes. Theacquired images may be analyzed in any of the ways described herein. Forexample, the acquired images may be analyzed by one or more of using aLine Scan Method in a step 145 a, using a Simple Boundary Method in astep 145 b, using a Reverse Watershed Method in a step 145 c, using aCircle Detection Method in a step 145 d, using a Combined ReverseWatershed and Circle Detection Method in a step 145 e, or using acombination of two or more of the aforementioned. A droplet may appearin more than one image of a Z-stack. In this case, the information inthose images may be combined by methods described herein above todetermine the diameter of that droplet. In a step 150, the acquiredimages may be analyzed for the presence of the target in the droplets.The analysis for the presence of the target may be performed in any ofthe ways described herein. The step 150 may, for example, comprise astep 150 a of detecting and analyzing for fluorescence. The step 150 mayoccur after the images are analyzed for droplet sizes in the step 145 ormay occur as a parallel step to step 145. The step 150 may include astep 150 a of detecting and analyzing for fluorescence. In a step 155,the target concentration in the sample may be calculated. The targetconcentration in the sample may be calculated in any of the waysdescribed herein. For example the calculation may be based on the imageanalysis for droplet size from the step 145 and the image analysis forthe target presence in the droplets from the step 150.

Although the above steps show the methods 1100 and 100 for targetdetection in accordance with many aspects and embodiments, a person ofordinary skill in the art will recognize many variations based on theteaching described herein. The steps may be completed in a differentorder. Steps may be added or deleted. Some of the steps may comprisesub-steps. Many of the steps may be repeated as often as beneficial.

One or more of the steps or sub-steps of the methods 1100 and 100 may beperformed with processing elements or circuitry as described here, forexample one or more of the processor or CPU 1005 of the computing device1001 of the system 1000 described herein. Instructions for the CPU 1005may be stored on the memory 1010 of the system 1000. These instructions,when executed by the CPU 1005, may perform one or more of the steps orsub-steps of the methods 1100 and 100.

In various aspects, the disclosure provides many methods for detectingor recognizing droplets such as the Line Scan Method, the SimpleBoundary Method, the Reverse Watershed Method, the Circle DetectionMethod, the Combined Reverse Watershed and Circle Detection Method, orcombinations thereof described herein. In some aspects, the methods ofdetecting or recognizing the droplets may be independent of the methodsto determine sample concentration. That is, the methods of detecting orrecognizing the droplets may be used for many purposes other thanperforming digital assay described herein.

FIGS. 2D, 2E, 2F, 2G, and 2H schematically illustrates exemplary dropletrecognition methods 1200, 1300, 1400, 1500, and 1600, respectively. Thestep 1140 may apply one or more of the methods 1200, 1300, 1400, 1500,and 1600 to analyze an image stack to detect or recognize droplets, forexample.

As shown in FIG. 2D, the droplet recognition method 1200 may be similarto or comprise the Line Scan Method described above and may comprisevarious steps as follows. In a step 1210, an appropriate threshold levelfor an individual image may be set. The appropriate threshold level maybe a pixel intensity threshold for example. In a step 1220, line scansmay be obtained within the image. In a step 1230, the line scans may beanalyzed for pixel sets. These pixel sets may comprise, for example,segments of the line scans which are at or outside the set thresholdlevel (e.g., above or below) and which are contiguous between adjacentline scans. In a step 1240, droplets may be identified from the pixelsets. For example, the longest segment of a line scan for a pixel setcan be regarded as the diameter of a droplet and the size of the dropletcan be calculated from the diameter. While line scans are generallydiscussed herein, other methods of generating scans are alsocontemplated. These methods may include confocal scanning, lineillumination and collection, Nipkow disc type scanning, or the like.

As shown in FIG. 2E, the droplet recognition method 1300 may be similarto or may comprise the Simple Boundary Method described above and maycomprise various steps as follows. In a step 1310, an appropriatethreshold level is set for an individual image. In a step 1320, areas ator outside the threshold level (e.g., above or below) may be identifiedas a pixel set(s). In a step 1330, the aspect ratios of the pixel set(s)may be measured. In a step 1340, pixels set(s) whose aspect ratio isoutside (e.g., generally below but may be above alternatively) athreshold aspect ratio are identified as single droplets. The thresholdaspect ratio may be 1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, or2.0, for example. In a step 1350, a list of droplet(s) for each imagecan be compiled.

As shown in FIG. 2F, the droplet recognition method 1400 may be similarto or may comprise the Reverse Watershed Method described above and maycomprise various steps as follows. In a step 1405, a 3D topological mapbased on the pixel intensities of an individual image may be generated.In a step 1410, the topological map may be filled with “water” (i.e., acomputerized, synthetic representation of water or other fluid) to abovethe “peaks” of topological map. The topological map can be filled with“water” in many ways as described herein above. For example, thestandard deviation of the signal within the background of each image canbe determined, multiplied with a signal-to-noise ratio, and then addedto the average intensity of a background pixel. In a step 1415, the“water level” may be lowered. The “water level” of the topological mapmay be lowered in many ways described herein above. For example, amaximum pixel intensity cutoff threshold may be established and lowereduntil it reaches the background pixel intensity threshold. In a step1420, “protrusions” or “islands” (i.e., highest intensity pixels) may betracked as the “water level: is lowered. In a step 1425, such“protrusions” or “islands” may be identified as Region(s) of Interest ifthey satisfy a user defined criteria such as a minimum required area.The user-defined criterion may be defined in many ways as describedherein above. In a step 1430, the Region(s) of Interest may be merged asthe “water level” is lowered depending if certain criteria, for exampleas described herein above, are met. As described herein above, the imagemay be smoothed prior to making the determination of whether to mergetwo or more Regions of Interest. In a step 1435, the lowering of the“water level” may end when a threshold is met. The threshold maycomprise a background intensity threshold or cutoff as described hereinand may be determined in many ways as described herein above.

In a step 1440, group(s) of connected pixels may be identified as PixelGroup(s). Such identification can be made in many ways as describedherein above. In a step 1445, gaps within the Pixel Group(s) may beidentified as holes or noise, such as by applying a hole threshold asdescribed herein above. The holes may comprise gaps between droplets,for example. In a step 1450, the Region(s) of Interest may be merged asthe “water level” is lowered or after the lowering of the “water level”is ended depending if certain criteria, for example as described hereinabove, are met. As described herein above, the image may be smoothedprior to making the determination of whether to merge two or moreRegions of Interest.

In a step 1455, a Pixel Group comprising only a single Region ofInterest may be identified as a droplet. In a step 1460, a circle may befit to the boundaries of the single Region of Interest. The circle maybe analyzed to obtain a droplet diameter as described herein above.Pixel Groups having multiple Regions of Interest may be identified inaccordance with the methods described herein above to identify mostprobably droplets. In a step 1465, the Regions of Interest within asingle Pixel Group may be fit with circles. In a step 1470, the best fitcircles may be identified as droplets. The best fit circles may beanalyzed to obtain droplet diameters as described herein above.

As shown in FIG. 2G, the droplet recognition method 1500 may be similarto or may comprise the Circle Detection Method described above and maycomprise various steps as follows. In a step 1510, a threshold may beapplied to an individual image. The threshold may be determined as inthe Reverse Watershed Method described herein above. In a step 1520,groups of connected pixels may be identified as Pixel Groups. Suchidentification may be made as in the Reverse Watershed Method describedherein above. In a step 1530, gaps within the Pixel Group(s) may beidentified as holes or noise such as by applying a hole threshold asdescribed herein above. In a step 1540, the external boundaries of thePixel Group(s) may be determined. In a step 1550, the Circle HoughTransform is applied to the boundaries of the Pixel Group(s). In a step1560, circles not meeting certain criteria may be eliminated. Thecriteria may be any of the criteria described herein above. In a step1570, one or more of the remaining circles may be accepted. Criteria maybe applied as described herein above to determine whether to accept theremaining circle(s). In a step 1580, the accepted remaining circles areused to find the best boundary pixels for a droplet. In a step 1590, theboundary pixels are fit to a circle to obtain a collection of best-fitcircles corresponding to the droplet(s). These best fit circles may beused to determine the diameters and sizes of the droplet(s).

As shown in FIG. 2H, the droplet recognition method 1600 may be similarto or may comprise the Combined Reverse Watershed and Circle DetectionMethod described above and may comprise various steps as follows. Thesteps 1605, 1610, 1615, 1620, 1625, 1630, 1635, 1640, and 1645 may besimilar to the steps 1405, 1410, 1415, 1420, 1425, 1430, 1435, 1440, and1445, respectively of the Reverse Watershed method 1400 described above.In a step 1605, a 3D topological map based on the pixel intensities ofan individual image may be generated. In a step 1610, the topologicalmap is filled with “water” (i.e., a computerized, syntheticrepresentation of water or other fluid) to above the “peaks” oftopological map. The topological map can be filled with “water” in manyways as described herein above. For example, the standard deviation ofthe signal within the background of each image can be determined,multiplied with a signal-to-noise ratio, and then added to the averageintensity of a background pixel. In a step 1615, the “water level” maybe lowered. The “water level” of the topological map may be lowered inmany ways described herein above. For example, a maximum pixel intensitycutoff threshold may be established and lowered until it reaches thebackground pixel intensity threshold. In a step 1620, “protrusions” or“islands” (i.e., highest intensity pixels) may be tracked as the “waterlevel: is lowered. In a step 1625, such “protrusions” or “islands” maybe identified as Region(s) of Interest if they satisfy a user definedcriteria such as a minimum required area. The user-defined criterion maybe defined in many ways as described herein above. In a step 1630, theRegion(s) of Interest may be merged as the “water level” is lowereddepending if certain criteria, for example as described herein above,are met. As described herein above, the image may be smoothed prior tomaking the determination of whether to merge two or more Regions ofInterest. In a step 1635, the lowering of the “water level” may end whena threshold is met. The threshold may comprise a background intensitythreshold or cutoff as described herein and may be determined in manyways as described herein above. In a step 1640, group(s) of connectedpixels may be identified as Pixel Group(s). Such identification can bemade in many ways as described herein above. In a step 1645, gaps withinthe Region(s) of Interest are identified as holes or noise, such as byapplying a hole threshold as described herein above. In a step 1650, theCircle Hough Transform is applied to the boundaries of each Region ofInterest.

The steps 1655, 1660, 1670, and 1675 may be similar to the steps 1560,1570, 1580, and 1590, respectively, above. In a step 1655, circles notmeeting certain criteria may be eliminated. The criteria may be any ofthe criteria described herein above. In a step 1660, the remainingcircles may be accepted. In a step 1665, the accepted remaining circlesmay be used to find the best boundary pixels for a droplet. In a step1670, the boundary pixels are fit to best-fit circles. These best fitcircles may be used to determine the diameters and sizes of thedroplet(s).

Although the above steps show the methods 1100, 1200, 1300, 1400, 1500,and 1600 of detecting droplets and/or analyzing droplet or emulsionsystems in accordance with various aspects of the disclosure, a personof ordinary skill in the art will recognize many variations based on theteaching described herein. The steps may be completed in a differentorder. Steps may be added or deleted. Some of the steps may comprisesub-steps. Many of the steps may be repeated as often as beneficial.

One or more of the steps of the methods 1100, 1200, 1300, 1400, 1500,and 1600 may be performed with the computing system 1000 as describedherein. Alternatively or in combination, the one or more steps of themethods 1100, 1200, 1300, 1400, 1500, and 1600 may be performed withcircuitry or logic circuitry such as a programmable array logic for afield programmable gate array, an application-specific integratedcircuit, or other programmable or application-specific logic circuitry.The circuitry may be programmed to provide one or more of the steps ofthe method 1100, 1200, 1300, 1400, 1500, and 1600, and the program maycomprise program instructions stored on a non-transient computerreadable memory or storage medium or programmed steps of the logiccircuitry.

Compositions and Kits for Performing Digital Assays

The present disclosure provides for compositions and kits for performingthe digital assays as described herein. In certain aspects, kits andassays are provided for performing digital PCR.

In various aspects, the present disclosure provides compositions andkits for performing a digital assay comprising: a first fluid; a secondfluid, wherein the first fluid and the second fluid are immiscible ineach other and are capable of forming an emulsion when agitated; asurfactant; and an amplification reagent.

In some aspects, the composition further comprises a sample. In certainaspects, the sample is a nucleotide. In further aspects, the compositionfurther comprises a detectable agent, wherein the detectable agent iscapable of labeling a sample. In some aspects, the sample is labeledwith a detectable agent. In further aspects, the compositions furthercomprise a detectable agent capable of binding a nucleic acid sample.

In various aspects, the compositions comprise an amplification reagentselected from a polymerase chain reaction (PCR) reagent, rolling circleamplification (RCA) reagent, nucleic acid sequence based amplification(NASBA) reagent, loop-mediated amplification (LAMP) reagent or acombination thereof. In some aspects, the amplification reagent is a PCRreagent. In certain aspects, the PCR reagent is selected from athermostable DNA polymerase, a nucleotide, a primer, probe, or acombination thereof.

In some aspects, the compositions further comprise a third fluid,wherein the third fluid is immiscible in the second fluid. In certainaspects, the compositions are capable of forming a double emulsion.

In various aspects, the first fluid is aqueous. In further aspects, thefirst fluid comprises the amplification reagent. In some aspects, thesecond fluid is an oil. In further aspects, the second fluid is an oil,and the second fluid is immiscible with the first fluid and the thirdfluid. In yet further aspects, the first fluid is different from thethird fluid. In other aspects, the third fluid is an oil and the thirdfluid is immiscible with the first fluid and the second fluid.

In some aspects, the compositions further comprise a fluid interfacemodification element. In certain aspects, the fluid interfacemodification element is a surfactant. In further aspects, the fluidinterface modification element is selected from a lipid, phospholipid,glycolipid, protein, peptide, nanoparticle, polymer, precipitant,microparticle, a molecule with a hydrophobic portion and a hydrophilicportion, or a combination thereof.

In certain aspects, the compositions further comprise a solidifying orgelling agent capable of converting one or more of the immiscible fluidsto a gel or solid.

In some aspects, the present disclosure provides compositions and kitsfor performing a digital assay, the composition or kit comprising: afirst fluid; a second fluid, wherein the first fluid and the secondfluid are immiscible in each other and are capable of forming anemulsion when physically agitated; a surfactant; and a PCR reagent. Infurther aspects, the PCR reagents are selected from a thermostable DNApolymerase, a nucleotide, a primer, probe, or a combination thereof. Inother aspects, the detectable agent is capable of binding a nucleic acidsample.

In certain aspects, the present disclosure provides compositions andkits for performing PCR comprising a first fluid and a second fluid,wherein the first fluid and the second fluid are immiscible in eachother, a nucleic acid primer, deoxyribonucleotides, an enzyme suitablefor the extension of the nucleic acid primer, a fluorescent label, and adetectable agent that is capable of binding a nucleic acid samplefollowing amplification.

In further aspects, the compositions and kits can further comprisesuitable buffering and stabilizing agents that are compatible with PCRamplification.

Where a range of values is provided, it is understood that eachintervening value, to the tenth of the unit of the lower limit unlessthe context clearly dictates otherwise, between the upper and lowerlimit of that range, and any other stated or intervening value in thatstated range, is encompassed within the disclosure provided herein. Theupper and lower limits of these smaller ranges can independently beincluded in the smaller ranges, and are also encompassed within thedisclosure, subject to any specifically excluded limit in the statedrange. Where the stated range includes one or both of the limits, rangesexcluding either or both of those included limits are also included inthe disclosure provided herein.

The specific dimensions of any of the apparatuses, devices, systems, andcomponents thereof, of the present disclosure can be readily varieddepending upon the intended application, as will be apparent to those ofskill in the art in view of the disclosure herein. Moreover, it isunderstood that the examples and aspects described herein are forillustrative purposes only and that various modifications or changes inlight thereof can be suggested to persons skilled in the art and areincluded within the spirit and purview of this application and scope ofthe appended claims. Numerous different combinations of aspectsdescribed herein are possible, and such combinations are considered partof the present disclosure. In addition, all features discussed inconnection with any one aspect herein can be readily adapted for use inother aspects, herein. The use of different terms or reference numeralsfor similar features in different aspects does not necessarily implydifferences other than those expressly set forth. Accordingly, thepresent disclosure is intended to be described solely by reference tothe appended claims, and not limited to the aspects disclosed herein.

Unless otherwise specified, the presently described methods andprocesses can be performed in any order. For example, a methoddescribing steps (a), (b), and (c) can be performed with step (a) first,followed by step (b), and then step (c). Or, the method can be performedin a different order such as, for example, with step (b) first followedby step (c) and then step (a). Furthermore, those steps can be performedsimultaneously or separately unless otherwise specified withparticularity.

While preferred aspects of the present disclosure have been shown anddescribed herein, it is to be understood that the disclosure is notlimited to the particular aspects of the disclosure described below, asvariations of the particular aspects can be made and still fall withinthe scope of the appended claims. It is also to be understood that theterminology employed is for the purpose of describing particular aspectsof the disclosure, and is not intended to be limiting. Instead, thescope of the present disclosure is established by the appended claims.In this specification and the appended claims, the singular forms “a,”“an” and “the” include plural reference unless the context clearlydictates otherwise.

All publications, patents, and patent applications mentioned in thisspecification are herein incorporated by reference to the same extent asif each individual publication, patent, or patent application wasspecifically and individually indicated to be incorporated by reference.

EXAMPLES

The specific dimensions of any of the apparatuses, devices, systems, andcomponents thereof, of the present disclosure can be readily varieddepending upon the intended application, as will be apparent to those ofskill in the art in view of the disclosure herein. Moreover, it isunderstood that the examples and aspects described herein are forillustrative purposes only and that various modifications or changes inlight thereof can be suggested to persons skilled in the art and areincluded within the spirit and purview of this application and scope ofthe appended claims. Numerous different combinations of aspectsdescribed herein are possible, and such combinations are considered partof the present disclosure. In addition, all features discussed inconnection with any one aspect herein can be readily adapted for use inother aspects herein. The use of different terms or reference numeralsfor similar features in different aspects does not necessarily implydifferences other than those expressly set forth. Accordingly, thepresent disclosure is intended to be described solely by reference tothe appended claims, and not limited to the aspects disclosed herein.

Example 1 Method for Generating Droplets of Variable Volumes in a Tube

This Example provides exemplary methods for the production ofpolydisperse droplets of variable volume according to one aspect of thepresent disclosure. In this example, PCR tubes are used, however, anysuitable vessel can be used according to the present disclosure.

FIG. 3 depicts the formation of an emulsion system by vortexingindividual tubes. In a Step 4A, the aqueous phase containing thereaction mixture was pipetted into a 0.2 mL PCR tube that was prefilledwith an appropriate oil-surfactant mixture. The oil phase consisted of73% Tegosoft DEC, 20% light mineral oil and 7% ABIL WE 09 surfactant,that were freshly mixed and equilibrated for at least 30 minutes beforeuse. Emulsions formed with this mixture showed superior thermostabilityduring standard emulsion PCR. In a Step 4B, after pipetting the aqueousphase to the oil mixture, droplets of variable size were formed byvortexing for about 30 seconds at about 3000 rpm. Emulsification wasfurther enhanced by adding a small stir bar to the mixture, whichpromoted breakup of the aqueous phase into smaller droplets duringvortexing. The presence of the surfactant in the oil stabilized theemulsion, which reduced the frequency of droplet fusion in the mixture.

A system containing both aqueous and oil phases was added to a smallcollection microtube containing a small stainless steel bead. The tubewas subsequently shaken at 15-17 Hz for 20 seconds to generate theemulsion. In a Step 4C, the emulsion was then transferred into a 0.2 mLPCR tube, and PCR was carried out in a Bio-Rad C1000 Thermal Cycler for3 minutes at 95° C. (a hot start) and 50 cycles of 30 seconds at 95° C.,30 seconds at 54° C., and 30 seconds at 72° C.

Example 2 Method for Generating Droplets of Variable Volume in aMulti-Well Plate

This Example provides a method for the production of polydispersedroplets of variable volume and subsequent modification and analysisaccording to one aspect of the present disclosure.

FIG. 4 depicts an optimized high-throughput process for droplet-emulsionPCR. After a multichannel pipette loads oil and aqueous PCR reagentsonto a multiwell plate, the entire multiwell plate is vortexed for 30seconds at 3000 rpm to induce emulsification. The multiwell plate issubsequently fitted with a thermal cycler adaptor, and the mixtureundergoes PCR amplification for 3 minutes at 95° C. (a hot start) and 50cycles of 30 seconds at 95° C., 30 seconds at 54° C., and 30 seconds at72° C. The multiwall plate is then removed from the thermal cycler andimaged with a fluorescence microscope, with no further sample transfersteps required. In this example, any droplet instability (e.g. fusion)following emulsification will be independent of mechanical handling.

Example 3 Determination of Best-Fit Circle

This Example provides a method for determining the best-fit circle fordroplets in a polydisperse droplet system. In this aspect, a set ofpixels, which are presumed to be some or the entire boundary of adroplet are fit to a circle using an existing optimization algorithm. Inthis aspect, the Nelder-Mead algorithm as implemented in MATLAB is used.The algorithm minimizes a fit error that is defined as in Equation (1)below:

$\begin{matrix}{E_{Fit} = \frac{\sum\limits_{p = 1}^{N_{p}}\left\lbrack {\sqrt{\left( {X_{p} - X_{trial}} \right)^{2} + \left( {Y_{p} - Y_{trial}} \right)^{2}} - R_{trial}} \right\rbrack^{2}}{R_{trial}^{2}}} & (1)\end{matrix}$

In this equation, X_(trial) and Y_(trial) correspond to the triallocation of the center of the circle for the current step in theoptimization procedure. R_(trial) is the trial radius of the circle forthe current step in the optimization procedure. There are N_(p) pixelsin the set of external pixels being fit with X_(p) and Y_(p) being thelocation of the pth pixel in the set. Therefore, the quantity inside thesquare root sign is the distance from the trial center to the pth pixel,from which the trial radius is subtracted to obtain an error. The erroris squared, summed over all pixels in the set and then divided by thesquare of the trial radius to obtain the fit error.

As part of the optimization, a count is made of the number of pixelsinside the Group that are also inside the current trial circle. If thenumber of pixels inside the circle (N_(C)) exceeds the number of pixelsthat are both inside the circle and inside the Group (N_(C,G)), then thecurrent trial location and radius are penalized by adding the following(as defined in Equation (2)) to the fit error:(N _(C) −N _(C,G))²  (2)

Addition the quantity from Equation (2) inhibits the optimization fromchoosing as a best-fit circle a circle that is too large and extendssignificantly outside the Group, as can occur when only a fraction of adroplet's boundary is being fit and noise causes that fraction toexhibit a curvature that is unrepresentative of the droplet. In somecases the methods use the fit error per pixel as part of the evaluationof the quality of the fit to droplets. The number of pixels in the fitis N_(p) and the fit error per pixel is defined in Equation (e) below:

$\begin{matrix}{E_{PerPixel} = {\frac{1}{N_{p}}\frac{\sum\limits_{p = 1}^{N_{p}}\left\lbrack {\sqrt{\left( {X_{p} - X_{trial}} \right)^{2} + \left( {Y_{p} - Y_{trial}} \right)^{2}} - R_{trial}} \right\rbrack^{2}}{R_{trial}^{2}}}} & (3)\end{matrix}$

In another aspect of the present disclosure, the mean square error isused in the evaluation of the quality of the fit to the droplets. Thisis defined in Equation (4) below:

$\begin{matrix}{E_{m\; s} = {\frac{1}{N_{p}}{\sum\limits_{p = 1}^{N_{p}}\left\lbrack {\sqrt{\left( {X_{p} - X_{trial}} \right)^{2} + \left( {Y_{p} - Y_{trial}} \right)^{2}} - R_{trial}} \right\rbrack^{2}}}} & (4)\end{matrix}$

Examples 4, 5 and 6 each reference the fitting of a circle to externalboundary pixels or feature pixels, which relates to the methodsdescribed in this example.

Example 4 The Reverse Watershed Method for Identifying Droplets

This Example describes an exemplary process for performing the ReverseWatershed Method according to an aspect of the present disclosure.

According to this aspect, an initial background cutoff for the image wascalculated by assuming that 40% of the image was background. For thisinitial background cutoff, 20% (equal to 40% divided by 2) is theestimated percentile of the image intensities that corresponds to themedian of the background pixel intensities. An estimated backgroundstandard deviation was calculated by assuming it was one half thedifference between the 20% percentile of the image and the 1% percentileof the image. The initial estimate of the background cutoff was then theestimated median plus twice the estimated standard deviation. Pixelswith intensities less than the initial estimate of the background cutoffwere selected for the next step. The average and standard deviation ofthe intensity of the selected pixels was calculated and the percentageof image pixels with intensities less than the average was determinedand found to be 22%. That percentage was compared with 20%, the initialestimate of the estimated percentile of image intensities thatcorresponds to the median of the background. These values were judged tobe in good agreement and the average and standard deviation of theselected pixels were accepted as the average and standard deviation ofthe background in the image for the purposes of calculating the SCT andBT. In the event those values had not been in good agreement, then a newinitial background cutoff would have been calculated by using 22% asthen estimated percentile of the image intensities that corresponds tothe median of the background pixel intensities and repeating theprocedure starting at the beginning of this paragraph.

The SCT for the image was then determined by multiplying the standarddeviation of the background calculated previously by asignal-to-noise-ratio and adding the result to the average intensity ofthe average background calculated previously. Here, the signal-to-noiseratio was selected as 3.2, however, this value can be adjusted by theuser depending on the amount of noise in the images.

A cutoff threshold was then selected that equaled the largest pixelintensity of the image. This cutoff threshold was lowered in 30 stepsuntil it reached the SCT. In this case, the steps were spaced at 904.0,872.0, 841.2, 811.5, 782.8, 755.1, 728.4, 702.7, 677.8, 653.8, 630.7,608.4, 586.9, 566.2, 546.1, 526.8, 508.2, 490.2, 472.9, 456.2, 440.1,424.5, 409.5, 394.5, 379.5, 364.5, 349.5, 334.5, 319.5, and 304.5. Thefirst value was equal to the largest pixel intensity in the image andthe last one was equal to the SCT for the image. A copy of the imagethat was smoothed was created for use in a later step. In this example,the smoothing was performed by MATLAB's conv2( ) function thatconvoluted the image with a smoothing structure defined (using MATLAB'snotation) as ‘[0.05, 0.10, 0.05; 0.10, 0.40, 0.10; 0.05, 0.10, 0.05]’.

At each step, imaging analysis software was used to find sets of pixels(hereafter referred to simply as a pixel set) in the image above thecurrent step's cutoff threshold. These pixel sets may comprise“protrusions” or “islands” from the “water level.” In this example,pixels were required to be 4-connected to be considered to be part ofthe same pixel set. If the area of such a pixel set equaled or exceededa user-defined criterion (i.e., 9 in this case), then it was marked as aregion of interest (ROI). In this case, the image was closed using theMATLAB routine, imclose( ), with a structuring element defined by theMATLAB expression strel(‘disk’, 1) before determining if the area of theset was of sufficient size. Once a ROI appeared in a particular locationof the image, its area was tracked as the cutoff threshold is decreased.The location of the maximum intensity pixel within each ROI and thevalues of the pixels within the ROI were also tracked.

As the cutoff threshold was lowered, it was possible for two or moreROIs to merge. A pixel set that is above a particular cutoff thresholdcan include two or more ROIs that were separate for a larger cutoffthreshold. This can happen because either: (i) the different ROIsrepresent different droplets that are so close together that theboundary region between them has a larger pixel intensity than thecurrent cutoff threshold or (ii) the amplitude of noise in the sample issufficiently large that two or more regions within a single dropletexhibit local maxima. These maxima can appear to the algorithm asseparate ROIs at larger cutoff thresholds.

A set of user-defined criteria was used to determine whether differentROIs whose areas were contained within the same pixel set of the currentstep should be merged and thereafter treated as one ROI or not mergedand tracked as separate ROIs. This determination was made depending on:(i) the distance between the maximum intensity pixels of the differentROIs and (ii) the values of the maximum intensity pixels of thedifferent ROIs, and. Other user-defined criteria could be applied aswell to make this determination.

In this example, for criterion (i) if the distance in maximum intensitypixels of the smoothed copy of the image was less than 5 pixels, thenthe two ROIs were merged and thereafter treated as a single ROI. In thisexample, for criterion (ii), if maximum intensity pixels haveintensities within 0.75 times the background standard deviation of thecutoff used to identify the current pixel set, then the two ROIs weremerged and thereafter treated as a single ROI. The reasoning is that iftwo previously separate ROIs appeared in the same pixel set for thecurrent cutoff value, then the pixels in the pixel set that lie betweenthe two maximum intensity pixels must have had intensities above thecurrent cutoff. Therefore if the maximum intensity in each of the twoROIs are both close to the current cutoff, the pixels in the pixel setthat lie between the two maxima must have had intensities close to themaxima. Therefore, the two ROIs were combined and were assigned to thesame droplet.

After the last step (i.e., the point at which the SCT has been used),the pixel sets were referred to as Pixel Groups. Where different ROIswhose areas were contained within the same Pixel Group were not merged,the unassigned pixels of that Pixel Group were assigned to an ROI.Specifically, a list of unassigned pixels within the Pixel Group wassorted by intensity, and the pixel with the largest intensity that wasimmediately adjacent to one and only one of the ROIs was assigned tothat ROI. This process was repeated until the only unassigned pixelsremaining were those that were immediately adjacent to two or moredifferent ROIs. Those pixels were left unassigned.

The Reverse Watershed Method was applied to the image in FIG. 1, whichis a gray-scale image of a polydisperse droplet emulsion system obtainedusing confocal fluorescent microscopy. As shown in FIG. 5A, the imagewas divided into groups that are separated by pixels whose intensity isbelow the background threshold. Some of the groups contain only a singleROI and some contain two or more. The boundary pixels depicted in FIG.5A are those pixels belonging to a group that were adjacent to anon-group pixel.

The resulting Pixel Groups were analyzed and the ROIs within them wereassigned to droplets and subjected to the following process steps, whichneed not necessarily occur in the order described below:

Step 1.

If a Group contained only a single ROI, then it was considered to be asingle droplet and its external boundary pixels were fit to a circle toobtain a droplet diameter.

Step 2.

For ROIs not yet assigned to a droplet, a best-fit circle to theexternal boundary pixels of that ROI was obtained as described inExample 3. Each unassigned ROI was then checked. If the number of pixelsof a ROI that were inside of the circle was at least 30% of the area ofthe circle, then a fit was performed combining the external boundarypixels of the ROI being checked with the external boundary pixels of anyadjacent ROI that is not already assigned to a droplet. Two ROIs wereconsidered “adjacent” when an interior boundary of one ROI is separatedby zero or one pixel from the interior boundary of the other. In FIG.5A, the ROIs that were separated by what appears as a double line areconsidered adjacent. The double line represents the two interiorboundaries that lay near each other. The combined set of externalboundary pixels were fit to a circle and the results were evaluated todecide if the two ROIs should be combined and considered to part of asingle droplet. The criteria for combining the two ROIs were: (i) thefit error per pixel for the combination of two ROIs was less than 0.12or the fit error per pixel was less than 1.5 times the fit error of theoriginal ROI being checked and (ii) the area of the two ROIs togetherinside the best-fit circle was at least 85% of the area of the area ofthe ROIs. If the two ROIs were combined, then they were thereafterdenoted as a droplet and treated as a single unit. The external boundarypixels of the droplet were then the set of external boundary pixels ofthe ROIs assigned to that droplet. This process was repeated with alladjacent ROIs.

Step 3.

If an unassigned ROI had no adjacent ROIs that were unassigned, then themethod fit the external boundary of that ROI to a circle. The ROI wasaccepted as a droplet if the fit error per pixel was less than 0.12 andthe area of the ROI inside the best-fit pixel was at least 60% of thearea of the circle.

Step 4.

This method then checked pairs of droplets to determine if they were infact portions of the same droplet. At this step it required that thebest-fit circle of the droplets being checked be similar in size to eachother. The method compared the distance between the centers of dropletsthat had already been found. It is possible that two regions identifiedas droplets at this stage were actually portions of the same droplet.The distance between the best-fit center of a pair of droplets wascalculated and if it was less than 20% of the best-fit radius of each ofthe droplets, then the pair was tested to see if they were actuallyportions of the same droplet. The external boundary pixels of the twodroplets were combined and the combined set of pixels was fit to acircle. The fit errors of the two droplets being considered was summedand divided by the number of pixels in the combined set of externalboundary pixels. The fit error per pixel of the combined set must beless than 1.5 times this quantity and also less than 0.12. In that case,the two droplets were combined and thereafter considered to be onedroplet. This process was repeated for all pairs of droplets.

Step 5.

Next, each Pixel Group was examined to determine if it had both dropletsand unassigned ROIs. If so, then for each droplet, the unassigned ROIswere examined and determined if at least 85% of a given ROI's area satinside the best-fit circle associated with the droplet. If so, then thatunassigned ROI was a candidate to be added to the droplet. Next acombined external boundary pixel set was made by combining the externalpixels of the droplet with the external boundary pixels of the ROI. Thecombined set was then fit to a circle. There were several criteria thatneeded to be satisfied before it was concluded that the ROI should beassigned to the droplet, these included: (i) the distance between thelocation of the best-fit circle of the combined set and the location ofthe best-fit circle of the droplet must be less than 3 pixels (thisdepends on a number of considerations primarily the size of the pixelsin the image); (ii) the distance between the location of the best-fitcircle of the combined set and the best-fit circle of the ROI must havebeen less than 20% of the radius of the best-fit circle of the ROI;(iii) the fit error per pixel of the combined set must have been lessthan twice the fit error per pixel for the ROI; (iv) the fit error perpixel of the combined set must have been less than 0.12 and (v) the meansquared error of the combined fit must have been less than 1.5 times themean squared error for the best-fit circle to the ROI. If all of thesecriteria were fulfilled, then the ROI was assigned to the droplet.

Step 6.

In this step, pairs of droplets were examined to determine if they areportions of the same droplet. In some aspects, the droplets making upthe pairs can have dissimilar diameters. The distance between thebest-fit center of a pair of droplets was calculated and if it was lessthan 50% of the best-fit radius of each of the droplets, then the amountof overlap of the two droplets area was calculated. If more than 60% ofthe area of each best-fit circle sat inside the other best-fit circle,then the external boundary pixels of the two droplets were combined andthe combined set of pixels was fit to a circle. The list of criteria thefit must satisfy is longer than in the previous step. A multiplierM_(err) was defined to be 1.5. Then, the fit errors of the two dropletsbeing considered was summed and divided by the number of pixels in thecombined set of external boundary pixels. The fit error per pixel of thecombined set must be less than times this quantity and also less than0.12. Next the mean squared error of the combined fit, MSE_(combined)was calculated. In addition, a new mean squared error was calculated foreach of the two droplets being checked, but instead of using thebest-fit circle of each droplet, the mean squared error for each dropletwas calculated by comparing the best-fit circle of the combined set ofpixels to the external boundary pixels assigned to each droplet.MSE_(combined) must be less than M_(err) times the new mean squarederror of each droplet. Finally, the best-fit location for the combinedset of pixels was invariably shifted from the best-fit location for eachof the two droplets being checked. The distance from the best-fitlocation of the first droplet to the best-fit location of the combinedset was determined. The difference must be less than 20% of the best-fitradius of the first droplet. The distance from the best-fit location ofthe second droplet to the best-fit location of the combined set wasdetermined. The difference must be less than 20% of the best-fit radiusof the second droplet. This was repeated for all pairs of droplets inthe image. If a pair of droplets was found to have satisfied all ofthese criteria, then those were combined and thereafter treated as asingle droplet. After all of the droplets had been checked, 0.35 wasadded to M_(err) and this entire step was repeated. Gradually increasingM_(err) led to droplets slowly being combined and reduced thepossibility of incorrect combination. This process continued forincreasing values of M_(err) up to 2.9.

Step 7.

This step involved the checking of pairs of droplets that hadsignificant overlap, regardless of whether they were of similar size. Amultiplier M_(err) was defined to be 1.5 and a minimum fraction F_(min)was defined to be 50%. The droplets of an image were ordered fromlargest to smallest by the ratio of the number of external boundarypixels to the circumference of the best-fit circle. Pairs of droplets(i, j) were checked, where i refers to the droplet with the largerradius and j refers to the droplet with the smaller radius. If at leastF_(min) of the area of droplet j was overlapped by the area of dropleti, then the pair was checked to see if they should be combined. Theexternal boundary pixels of the two droplets were combined into a setthat was fit to a circle. A number of criteria must be met in order toconclude that the two droplets should be combined, including thefollowing: (i) the fit error per pixel for the combined fit must be lessthan 0.12; (ii) the fit error per pixel of the combined fit must be lessthan M_(err) times the fit error per pixel of the best-fit circle fordroplet j; (iii) the mean squared error of the combined fit must be lessthan M_(err) times the mean squared error for the best-fit circle fordroplet j and (iv) the distance between the best-fit location of thecenter of the circle for the combined fit and the best-fit circle fordroplet j must be less than 20% of the best-fit radius of droplet j. Ifall these criteria were met, then droplets i and j were combined andconsidered one droplet.

Step 8.

In this step, each Pixel Group was examined and determined if it hadboth droplets and unassigned ROIs. If so, then for each droplet, itexamined each unassigned ROI and determined if at least 85% of the ROI'sarea lay inside the best-fit circle associated with the droplet. If so,then that unassigned ROI was a candidate to be added to the droplet.Next a combined external boundary pixel set was made by combining theexternal pixels of the droplet with the external boundary pixels of theROI. The combined set was fit to a circle. This step has a set ofcriteria that must be satisfied if an ROI is to be added to the droplet,including the following: (i) the fit error per pixel of combine fit mustbe less than 1.2 times the fit error per pixel of the fit error for theROI and (ii) the distance between the location of the center of thebest-fit circle to the combined set and the location of the center ofthe best-fit circle to the ROI must either be less than 1.4 pixels orless than 20% of the radius of the best-fit circle to the ROI. If thesecriteria were met, then the ROI was assigned to the droplet.

Step 9.

At this stage it was still possible that the ROIs assigned to a dropletdo not completely describe the circumference of the droplet. Thedroplets of an image were ordered from largest to smallest by the ratioof the number of external boundary pixels to the circumference of thebest-fit circle. For each Pixel Group, pairs of droplets each of whichhad a ratio less than 0.5 were examined. This step had some criteriathat were required to be met before the droplets were considered furtherfor consolidation. The amount of overlap between the best-fit circles ofthe two droplets was calculated. The distance between the centers of thetwo best-fit circles was calculated. The criteria included thefollowing: (i) the size of the overlap must exceed 30% of the area ofboth circles; (ii) the distance between the two circles must be lessthan 20% of the best-fit radius of whichever best-fit circle is largerand (iii) the difference in best-fit radius between the two best-fitcircles must be less than 30%. If these criteria were satisfied, thenthe external boundary pixels of the two droplets were combined andcircle was fit to the combined set. This procedure was repeated for allpairs of droplets.

Step 10.

For each droplet, the ratio of the number external pixels to thecircumference of the best-fit circle was then calculated and any dropletfor which this ratio does not exceed 0.65 was removed fromconsideration.

Step 11.

For each Pixel Group, a list of all ROIs that were still not assigned toa droplet was prepared. Then for each unassigned ROI, the methodsearched for the droplet with which it had the greatest overlap. If thesize of that overlap exceeded 50% of the area within the ROI, then themethod examined whether the ROI should be assigned to the droplet. Itcalculated the area inside the best-fit circle of the droplet that wasnot occupied by a ROI assigned to the droplet. If the area of theunassigned ROI was less than 1.05 times the area of the unoccupied areainside the droplet's best-fit circle, then external boundary pixels ofthe droplet and the unassigned ROI were combined to make a combined setof external boundary pixels. This combined set was then fit to a circle.This step has a set of criteria which must be satisfied before an ROIcan be added to the droplet including the following: (i) the fit errorper pixel of combine fit must be less than 1.2 times the fit error perpixel of the fit error for the ROI; (ii) the distance between thelocation of the center of the best-fit circle to the combined set andthe location of the center of the best-fit circle to the ROI must eitherbe less than 1.4 pixels or less than 20% of the radius of the best-fitcircle to the ROI or (iii) the fit error per pixel of the fit error perpixel for the combined set must be less than 0.12. If these criteriawere met, then the ROI was assigned to the droplet.

Step 12.

Any ROIs without any external boundary pixels were then assigned to thatdroplet if they were inside the best-fit circle of a droplet.

FIG. 5B shows the final, processed image prepared by the methods in thisexample. The image in FIG. 5B corresponds to FIGS. 1 and 5A and includesthe best-fit boundaries for those droplets that can be identified asdroplets. The image of FIG. 5B can then be used to determine dropletsize and target molecule presence for each given identified droplet.

Example 5 Circle Detection Method for Identifying Droplets

This Example describes an exemplary process for performing the CircleDetection Method according to an aspect of the present disclosure.

According to this aspect, the SCT was calculated as described above inExample 4 for the Reverse Watershed Method, except that thesignal-to-noise ratio was 2.5 (rather than 3.2 in Example 4). This SCTwas applied to an image to define Pixel Groups within the image. Thevalue of the SCT was also used to identify holes within each PixelGroup. The Pixel Group was checked for 8-connected sets of pixels whoseintensity was below the SCT inside the Pixel Group. If the set contained9 or more pixels it was denoted a Hole. The list of any pixels within aPixel Group that were adjacent to a Hole was added to the list ofexternal boundaries of the Pixel Group. The external boundaries of thePixel Groups were trimmed to eliminate noise pixels. The list of trimmedexternal boundary pixels includes only those external boundary pixels ofthe Pixel Group that were adjacent to at least one interior pixel. Thetrimmed external boundary pixels will also be referred as feature pixelsin this example. The Circle Hough transform was applied to the list offeature pixels of each Group.

The transform was performed for circle radii ranging from 3 to 60 pixelsfor each Pixel Group. According to this aspect, the standard transformmethod was modified to account for significant levels of noise in theimage. This modification can optionally be performed, depending upon thenoise characteristics of the images used. The number of votes assignedto a pixel was the weight assigned to the possibility that the pixel wasthe center of a circle of radius R. Ordinarily, for a given radius R,this value is simply the number of feature pixels within a distance R ofthe pixel. In this method it was the number of feature pixels within adistance R−1 to R+1 of the center of the circle. The number of votes fora particular center location and the list of feature pixels voting foreach center location were calculated for each value of R. The circlesfound by the Circle Hough Transform will be referred to as “H-circles”in this example to distinguish them from best-fit circles that wereobtained when a list of external pixels is fit to a circle. The latterare referred to as “circles.”

The list of H-circles generated for each Pixel Group was reduced asfollows. H-circles with fewer than 9 votes were discarded. AlsoH-circles for which the ratio of the number of votes to thecircumference of the H-circle was less than 0.40 were discarded.H-circles that contained any Hole pixels were discarded. Next the pixelsthat comprised the circumference of the H-circle were identified and thenumber of them that were in the image was counted (a H-circle can extendoutside of the image). The criteria applied at this point were asfollows: (i) the number of circumference pixels in the image, N_(CI),must exceed 14; (ii) the ratio of N_(CI) to the number of pixels in thecircumference must exceed 0.60 and (iii) the ratio of the number ofvotes for the H-circle to N_(CI) must exceed 0.50. If the H-circlepassed these criteria, then the fraction of the circumference that wasin the background of the image was checked. If that fraction was lessthan 0.15, then the H-circle was accepted at this stage. If the fractionwas not less than 0.15, but the radius was 5 or less, then the fractionof the H-circle's area that lays more than 1 pixel away from a pixel inthe group was calculated. If the H-circle's radius was 4 or 5 and thefraction is 0.15 or less, then the H-circle was accepted at this stage.If the H-circle's radius was 3 and the fraction is 0.20 or less, thenthe H-circle was accepted at this stage.

The ratio of the number of votes for an H-circle to the number ofcircumference pixels in the image was calculated for the H-circles stillaccepted at this stage. The H-circles were sorted by this ratio startingwith the largest and then descending in size. Each H-circle was comparedagainst all the H-circles with a smaller value of that ratio. If thecenters of the H-circles were within √{square root over (10)} pixels ofeach other and the radii of the H-circles differ by less than four, thenthe H-circle with the smaller value of the ratio was rejected. The imagein FIG. 1 was analyzed by this method and the results to this stage areshown in FIG. 6A. There were overlapping H-circles at this stage.

In this example, the next step was to reject H-circles that were a poorrepresentation of any droplet and then combine circles that were judgedto represent portions of the same droplet. Each H-circle was associatedwith the set of external boundary pixels that voted for that H-circle.The list of feature pixels for each H-circle was fit to a circle and themean squared error for the fit was calculated. At this point eachH-circle defined a set of pixels that were fit to obtain a best-fitcircle (BF-circle). For the additional analyses in this example, if aBF-circle was rejected, then the H-circle associated with it was alsorejected. If a BF-circle was assigned to a droplet, then the associatedH-circle was assigned to the same droplet. If the mean squared errorexceeded 0.70, then the BF-circle was rejected. It was observed thatsome of the larger droplets in the sample had extremely irregularexternal boundaries. This was ascribed to the refractive index mismatchbetween the contents of the droplets and the continuous medium thatsurrounded them. Small droplets located between the large droplet andthe microscope objective are capable of acting as lenses and thusdistort the image of the large droplet's boundary. To prevent this fromcausing a premature rejection of larger BF-circles, the above criterionwas relaxed for larger BF-circles. If the number of votes (i.e., N_(F)external boundary pixels fit to a circle) was greater than 30, then theBF-circle was rejected if the mean square error of the fit exceeded0.70+0.03×(N_(F)−30).

Next, the amount by which the area of pairs of BF-circles overlapped wascalculated and a list compiled of pairs where the area of overlap wasgreater than 65% of the area of one of the two BF-circles. For eachpair, the fraction of area inside the circle that was part of the PixelGroup was calculated, and the fraction of votes for each circle thatwere unique (were not also votes for the other circle) was calculated.If the fractions calculated for one BF-circle were both smaller than thecorresponding fractions for the other, then the first BF-circle wasrejected.

For the pairs for which neither BF-circle had been rejected and that haddifferent areas, another test was applied. The number of pixels that areinside the smaller BF-circle but not inside the larger BF-circle wascalculated. If that number was less than half the number of votes forthe smaller BF-circle, then the smaller BF-circle was rejected.

For the pairs for which neither BF-circle had been rejected to thispoint the distance between the centers of the BF-circles was calculatedand the difference between the radii of the two BF-circles wascalculated. If the distance between the centers was less than 2.1 pixelsand the difference between the radii was less than 2.1 pixels, then theBF-circle with the smaller number of votes was rejected.

Next, for each BF-circle, the number of unique votes was calculated.Unique votes are votes that are not also a vote for any other BF-circlethat had not itself been rejected previously. If the number of uniquevotes was less than 10 or the ratio of unique votes to the total numberof votes was less than 0.40, then that BF-circle was rejected.

For each Pixel Group a list of external Pixel Group boundary pixels thatwere not assigned to any H-circle (unassigned) was compiled. If thefraction of unassigned pixels was less than 10% of the total number ofexternal Pixel Group boundary pixels then the rejected H-circles werereexamined. For each of them, a list of unique votes (votes that werenot part of any accepted H-circle) was compiled. If the number of suchvotes exceeded 60% of the circumference of the rejected H-circle, therejected H-circle was restored to the list of accepted H-circles. AllH-circles accepted at this point were provisionally considered to bedroplets.

Next, each possible pair of droplets in a Pixel Group was examined,these are referred to respectively as “droplet one” and “droplet two”below. The number of unique votes (i.e., votes for one droplet that arenot votes for the other) was calculated for every droplet in every pair.The number of unique votes are denoted N_(U1) and N_(U2) for droplet oneand droplet two, respectively. If either of these numbers were less than9, then the pair was subjected to additional tests. For these tests. thedistance (d) between the best-fit centers of the droplets wascalculated. Also, for these tests, the area-inside denotes the pixelsthat are both inside the best-fit circle and also in the Pixel Group.Then four additional quantities were calculated. These were the ratio ofd to the best-fit radius of droplet one (D₁), the ratio of d to thebest-fit radius of droplet two (D₂), the fraction of the area-insidedroplet one that is not inside droplet two (F₁), and the fraction of thearea-inside droplet two that is not inside droplet one (F₂). It shouldbe noted that the terminology used in this example applies only to thisexample.

The following additional Conditions and Tests were applied:

Condition A: if N_(U1) and N_(U2) were both less than 9, then Test A wasperformed. Test A. If both D₁ and D₁ were both less than 0.3, then thedroplet with the smaller best-fit radius was rejected.

Condition B: if Condition A did not apply and N_(U1) was less than 9,then Test B was performed. Test B: if F₁ was less than 0.4, then dropletone was rejected.

Condition C: if Conditions A and B did not apply and N_(U2) was lessthan 9, then Test C was performed. Test C: if F₂ was less than 0.4, thendroplet two was rejected.

Condition D: if none of Conditions A, B or C applied, then a two-partTest D was applied. Test D, Part 1: if N_(U1) was less than N_(U2), andif D₁, D₂ and F₁ were all less than 0.3, then droplet one was rejected.If not, then Test D, Part 2 was applied. Test D, Part 2: if N_(U2) wasless than N_(U1) and if D₁, D₂ and F₂ were all less than 0.3, thendroplet two was rejected.

Condition E: if none of Conditions A, B, C or D applied, then Test E wasapplied. Test E: the fraction of unique area pixels was calculated that,for the purposes of this test, was defined as the fraction of the areainside a droplet that is not inside any other droplet in the PixelGroup. The fraction of overall unique votes was calculated, which forthe purposes of this test was defined as the fraction of votes for adroplet that were not votes for any other droplet in the Pixel Group. Ifboth fractions for droplet one were smaller than the correspondingfractions for droplet two, then droplet one was rejected. If bothfractions for droplet two were smaller than the corresponding fractionsfor droplet one, then droplet two was rejected.

Next each droplet in the Pixel Group was examined individually. A listof pixels that are part of the best-fit circumference of the droplet andwithin the image was constructed. The fraction of those pixels that wereinside the Pixel Group, but not coincident with or adjacent to anexternal boundary pixel (F_(C)) was calculated. If F_(C) exceeded 60%,then the droplet was rejected.

If F_(C) exceeded 0.3 and the number of pixels that were inside thePixel Group, but not coincident with or adjacent to an external boundarypixel was greater than 2, then a different test was performed. Two setswere created from the list of pixels that were part of the best-fitcircumference of the droplet. The first set (set one) consisted of thosepixels that were coincident with or adjacent to a vote assigned to thedroplet. The second set (set two) consisted of those pixels that wereinside the Pixel Group, but not in set one. The average (A₁) andstandard deviation (S₁) of the intensities of the pixels in set one werecalculated. The average (A₂) of the intensities of the pixels in set twowere calculated. If A₁+(2−F_(C))×S₁<A₂, then the droplet was rejected.In some cases, noise distorting the external boundary of a dropletresults in H-circles that are significantly smaller than the droplet. Inthose cases, the portion of the BF-circle's circumference that lies inthe interior of the droplet can have an average intensity that issignificantly larger than the portion that lies near the externalboundary of the Pixel Group. This test was used to identify and rejectthose H-circles.

Next, for each droplet, the list of pixels-inside (i.e., pixels that areinside the best-fit circle and inside the droplet) was constructed andthe intensities of those pixels were analyzed. If the 90th percentile ofthose intensities was less than the average background intensity plus 5times the standard deviation of the background intensities, then thedroplet was rejected. If the number of pixels-inside that hadintensities greater than the average background intensity plus 3.5 timesthe standard deviation of the background intensities (N_(3.5)) was fewerthan 4, then the droplet was rejected. The fraction of pixels-insidewhose intensity was above the average background intensity plus 3.5 wasalso calculated (F_(3.5)). If F_(3.5) was less than 0.10, the dropletwas rejected. If F_(3.5) was less than 0.15 and N_(3.5) was less than20, the droplet was rejected.

The droplets were reexamined at that point. If the number of uniquevotes (votes for a droplet that are not also votes for a differentdroplet) was less than 5, the droplet was rejected. If the number ofunique votes was less than 9 and the mean squared error of the fit wasmore than 0.25 and the fit error is more than 0.4, then the droplet wasrejected.

An attempt was then made to assign any external Pixel Group boundarypixels to droplets. For each droplet, any external Pixel Group boundarypixels that were inside or adjacent to the best-fit circle of a dropletwere provisionally added to the list of votes (pixels that were used toobtain a best-fit circle) of that droplet. Pixels that were added tomore than one droplet by this procedure were removed from the list ofvotes assigned to those droplets.

A best-fit circle was then obtained using the revised list of votes foreach droplet.

Next each droplet in the Pixel Group was examined individually. A listof pixels that are inside the best-fit circle of a droplet, part of theGroup, but not part of another droplet was compiled. If the number ofthose pixels was less than 75% of the total number of pixels inside thebest-fit circle of a droplet and inside the Pixel Group, then thefollowing two tests (Tests F and G) were applied.

Test F: a list of pixels that were part of the best-fit circumference ofthe droplet and within the image was constructed. The fraction of thosepixels that were inside the Pixel Group, but not coincident with oradjacent to an external boundary pixel (F_(C)) was calculated. If F_(C)exceeded 60%, then the droplet was rejected.

Test G: if F_(C) exceeded 0.3 and the number of pixels that were insidethe Pixel Group, but not coincident with or adjacent to an externalboundary pixel, was greater than 2, then a different test was performed.Two sets were created from the list of pixels that were part of thebest-fit circumference of the droplet. The first set (set one) consistedof those pixels that were coincident with or adjacent to a vote assignedto the droplet. The second set (set two) consisted of those pixels thatwere inside the Pixel Group, but not in set one. The average (A₁) andstandard deviation (S₁) of the intensities of the pixels in set one werecalculated. The average (A₂) of the intensities of the pixels in set twowere calculated. If A₁+(2−F_(C))×S₁<A₂, then the droplet was rejected.In some cases, noise distorting the external boundary of a dropletresults in best-fit circles that are significantly smaller than thedroplet. In those cases, the portion of the best-fit circle'scircumference that lies in the interior of the droplet can have anaverage intensity that is significantly larger than the portion thatlies near the external boundary of the Pixel Group. This test was usedto identify and reject those droplets.

If the mean squared error exceeded 1.0, then the BF-circle was rejected.However, if the number of votes (N_(F) external boundary pixels fit to acircle) was greater than 30, then this requirement was relaxed anddroplet was rejected if the mean square error of the fit exceeded1.0+0.03×(N_(F)−30).

If the max fit error per pixel exceeded 0.10, then the droplet wasrejected.

The fraction of the votes for a droplet whose distance to the best-fitcenter is within ±1.16 pixels of the best-fit radius is calculated(F_(G)). Also the ratio of votes for a droplet to the size of thatportion of the best-fit circumference that lay in the image wascalculated (F_(VC)). If F_(G) was less than 0.5 and F_(VC) was less than0.575, the droplet was rejected.

For each droplet, the list of pixels-inside (pixels that are inside thebest-fit circle and inside the Pixel Group) was constructed and theintensities of those pixels was analyzed. If the 90th percentile ofthose intensities was less than the average background intensity plus 5times the standard deviation of the background intensities, then thedroplet was rejected. If the number of pixels-inside that hadintensities greater than the average background intensity plus 3.5 timesthe standard deviation of the background intensities (N_(3.5)) was fewerthan 4, then the droplet was rejected. The fraction of pixels-insidewhose intensity was above the average background intensity plus 3.5 wasalso calculated (F_(3.5)). If F_(3.5) was less than 0.10, the dropletwas rejected. If F_(3.5) was less than 0.15 and N_(3.5) was less than20, the droplet was rejected.

The procedure of this example was applied to the image in FIG. 1. Theintermediate result of this method is shown in FIG. 6A and the best-fitcircles for the droplets accepted is shown in FIG. 6B.

Example 6 Combined Reverse Watershed and Circle Detection Methods forIdentifying Droplets

This Example describes an exemplary process for performing the CombinedReverse Watershed and Circle Detection Methods according to an aspect ofthe present disclosure.

According to this aspect, the ROIs, Pixel Groups, and external boundarypixels were determined using the Reverse Watershed Method, after whichthe Circle Hough Transform was applied to the boundary pixels. Byperforming these methods in combination, additional criteria wereapplied in sorting the ROIs within a group into droplets. Threedifferent cutoffs were defined for this example. The average andstandard deviation of the background were calculated as described inExample 4. These will be referred to in this example as the initialaverage and initial standard deviations. The SCT for this example wasthe initial average plus 2.5 times the initial standard deviation. Thecutoff for holes was the initial average plus 2.75 times the initialstandard deviation. One further cutoff was applied to determine whichpixels were parts of the background. The background cutoff was theinitial average and 2.3 times the initial standard deviation of thebackground. The use of a smaller cutoff to define the background was toeliminate areas of the image that contained fluorescence that originatedfrom other focal planes in the sample. All pixels whose intensities wereless than the background cutoff were considered to be part of the finalbackground.

In addition, all 4-connected sets of pixels with intensities greaterthan the background cutoff were examined. If the area of the set wasless than 10 pixels, then those pixels were included in the finalbackground. The pixels in the final background were used to calculatethe final average background intensity that was used to obtainbackground subtracted intensities.

In this example the cutoff using the SCT was applied first to definegroups, as in Example 5. In addition each Pixel Group was checked for8-connected sets of pixels whose intensity was below the hole cutoff(HT) inside the Pixel Group. If the set contained nine or more pixels itwas denoted a Hole. The list of any pixels within a Pixel Group thatwere adjacent to a Hole was added to the list of external boundaries ofthe Pixel Group. Then the Reverse Watershed method was applied to theimage as in Example 4. By determining the Pixel Groups first, any ROIsfound by the Reverse Watershed method were then immediately collectedinto the Pixel Group to which they belong. This was done for bookkeepingpurposes and was not essential. The external boundaries of the ROIs weretrimmed to eliminate noise pixels. The list of trimmed external boundarypixels includes only those external boundary pixels of the ROI that areadjacent to at least one interior pixel. An interior pixel is one thatpart of a Pixel Group, but is not adjacent to a non-group pixel.

The list of trimmed external boundaries is referred to below as the listof feature pixels. In contrast to Example 4, the Reverse Watershedmethod, the trimmed external boundary pixels of each ROI were not fit toa circle at this stage. Instead, the Circle Hough transform was appliedto the list of feature pixels of each ROI. The transform was performedfor circle radii ranging from 2 to 60 pixels for each Pixel Group. Amodified method for performing the transform was used in this exampledue to the elevated level of noise in the image. The number of votesassigned to a pixel in this aspect was the weight assigned to thepossibility that the pixel is the center of a circle of radius R.Ordinarily, for a given radius R, the number of votes assigned to apixel would instead be the number of feature pixels within a distance Rof the pixel. In this method it was the number of feature pixels withina distance R−1, R or R+1 of the center of the circle. The number ofvotes for a particular pixel and the list of feature pixels voting foreach pixel were calculated for each value of R.

The list of circles generated for each ROI was reduced as follows: (i)if the fraction of the circle occupied by pixels that are not part ofthe Pixel Group to that the ROI belongs (non-Pixel Group pixels) exceeds30% the circle is rejected; (ii) if the ratio of the number of non-Grouppixels inside the circle to the circumference of the pixel exceeds 0.40the circle is rejected; (iii) if the fraction of the circumference ofthe circle that are non-Pixel Group pixels exceeds 70% the circle isrejected and (iv) if the ratio of the non-Pixel Group pixels inside thecircle to Pixel Group pixels inside the circle exceeds 0.30 the circleis rejected.

The pairs of circles with the same radius were then examined. If thedistance between the centers of the circles was less than 50% of theradius (or less than 2 pixels for radii <5 pixels) then the lists ofpixels voting for each of the two circles were compared. If there was anoverlap of more than 30% (the number of votes in common with bothcircles is 30% or more of either of the two lists), then the circle withthe smaller number of votes was rejected.

Next, the pairs of circles that could have different radii wereexamined. If the distance between the centers of the circles was lessthan 50% of the radius of the larger circle, then the lists of pixelsvoting for each of the two circles were compared. If there was anoverlap of more than 30% (the number of votes in common with bothcircles is 30% or more of the list for the circle with the smallerradius) then the circle with the smaller radius was rejected.

The circles associated with an ROI at that point were sorted by thenumber of votes, starting with the largest number of votes. Then eachcircle was compared with all other circles associated with the ROI withfewer votes (referred to below as the circle A and B, respectively). If50% or more of the votes for the circle B were also votes for circle A,then two additional checks were performed for that pair of circles. If60% or more of the area inside the circle B was also inside circle A,then the circle B was rejected. If either circle overlapped the edge ofthe image, then the areas considered was only that portion of the areaof the circle that was in the image. For the additional inquiry, thedistance between the centers of the two circles was calculated. If thisdistance was less than 89% of the radius of the larger of the twocircles, then circle B was rejected. The next step according to thisaspect was to group ROIs into droplets using the circles identified forthem.

If a Pixel Group had only a single ROI circle left at this point, thenthat circle was used to identify the external boundary pixels used tosize the droplet.

If there were two or more circles a set of tests was then performed. Foreach circle the distance from its center to the centers of all othercircles in the Pixel Group was calculated and then divided by the radiusof the first circle (ΔC_(scaled)). A list of all circle pairs wascreated and sorted by ΔC_(scaled) starting with the smallest. IfΔC_(scaled) for a pair of circles was less than 0.10 and the ratio ofthe difference in radius for the two circles to the radius of thesmaller circle was less than 0.20, then the two circles (and the ROIsthey are associated with) were assigned to be part of the same droplet.Any remaining circles at this stage that had not been assigned to adroplet were each assigned to a separate droplet. Next, a list of thevotes associated with a droplet was created. This of votes included allthe votes for the circles assigned to the droplet. This list was thenfit to a circle.

It is possible that a single ROI could have been assigned to more thanone droplet. This was checked for and in those instances, the distancefrom the best-fit center of each droplet to the center of the circleassociated with the ROI was calculated. The ROI was assigned to thedroplet for which this distance was smallest and removed from the listof circles assigned to the droplet for which this distance was largest.This step of the example assumes that the each ROI found by the ReverseWatershed Method was only part of one droplet. If this step leaves adroplet without any ROIs assigned to it, then that droplet was rejected.A list of droplets associated with a Pixel Group was created and sortedby radius, starting with the largest radius. Then all pairs of dropletswithin a Pixel Group were compared. If 75% or more of the pixels insidethe best-fit circle with the smaller radius were also inside thebest-fit circle with the larger radius, then the droplet with thesmaller best-fit radius was rejected and any ROIs assigned to therejected droplet were assigned to the droplet with the larger radius.

Next, if there were any unassigned ROIs in the Pixel Group, they werechecked to see if they should be assigned to an existing droplet. Thepixels for circumference of a droplet (determined by fitting a circle tothe droplet's votes) was dilated using MATLAB's imdilate( ) function anda structuring element defined by the MATLAB expression strel(‘square’,3) to produce a mask. For each unassigned ROI, if 50% or more of itstrimmed external boundary pixels was within that mask, then that ROI wasassigned to the droplet. The pixels of the ROI that were inside the maskwere added to the votes for that droplet. Any droplet whose list ofassigned ROIs was changed by these steps was refit to a circle. If aPixel Group was then found to have no droplets associated with them atall, then the trimmed external boundary pixels were fit to a circle andthe entire Pixel Group treated as one droplet.

In other aspects, alternate methods could be used to locate additionaldroplets within the image. If a Pixel Group had a significant number ofpixels that were not inside a droplet, the external boundary pixels ofany ROIs that were not already assigned to a droplet could be fit to acircle. Additional constraints can be applied in that in addition to nothaving a significant overlap with the non-group pixels, these additionalcircles can be constrained to not have significant overlap with existingdroplets within the group.

The problem of the region between two droplets having elevated pixelintensities leading to a non-circular boundary was mitigated by the useof the Circle Hough Transform, since it discriminated against pixelsthat form a non-circular boundary.

FIG. 7A shows a processed image produced after the Reverse Watershed andCircle Hough Transform methods were applied to the image of FIG. 1 andunwanted circles rejected. FIG. 7B shows the final results obtainedafter sorting those circles to identify and locate droplets.

Example 7 dPCR Amplification and Analysis

This Example describes a method for dPCR amplification and analysis of anucleotide sample using a polydisperse droplet emulsion system.

In order to visualize the presence of amplification products within adroplet, a fluorescence probe was added to the reaction mixture thatspecifically recognized the presence of the amplicon. A small amount(1-2 μM) of the red fluorescent dye 6-carboxy-X-rhodamine (ROX) was usedas a reference dye in the reaction mix. The spectral signature of ROX isreadily distinguished from that of a green fluorescence probe used toreport amplification. Furthermore, the ROX fluorescent signal isinsensitive to amplification or other reaction or reagent conditions.The ratio of two intensities, one measured from the reference dye andone measured from the probe, is used to make a binary measurement fromeach measured droplet. The intensity ratio is not affected by changes indroplet volume due to fusion or shrinkage, or unwanted changes in lightexcitation power, since each of these will affect fluorescence intensityof both dyes comparably, leaving the ratio unchanged.

In order to build a profile of the distribution of droplet sizes, theemulsion was transferred onto a 96-well plate, the surface of which wassilanized, and covered with an excess volume of the oil-surfactantmixture. Emulsions were imaged using a Zeiss LSM 510 confocal microscopein multi-track mode with a PLAN APO 20×, 0.75 NA objective. Laser-sourceexcitation wavelengths of 543 nm (LP 610) and 488 nm (BP 500-530) wereused to collect fluorescence signals from the ROX and FAM dyes. For eachfield of view, a series of optical sections (z-stacks) were imaged atvarying depths along the z-axis to build a 3D profile of dropletdimensions.

FIGS. 8A-8C illustrate a rapid method for verifying the presence of PCRamplification products in droplets during data acquisition. Circles inFIGS. 8A and 8B indicate identified droplets. Graphs on the right ofFIGS. 8A and 8B depict fluorescence intensities along the straight linesdepicted in the images on the left. Fluorescence intensity was measuredacross a line through the center of two droplets with similar diametersin the red fluorescent (ROX) and green fluorescent (FAM) channels (FIGS.8A and 8B, respectively). Some, but not all, of the ROX-labeled dropletswere also labeled with a green fluorescent DNA reporter. Both dropletshad similar red fluorescence intensities whereas the green fluorescenceintensity of droplet (2) was about 2.5 times greater than droplet (1).The lower signal of droplet (1) was consistent with backgroundintensities generated by the TaqMan probe, which comprises the FAMfluorophore, indicating the absence of target DNA in droplet (1). Thehigher signal in droplet (2) observed in the FAM channel indicated thatamplification took place in that droplet.

FIG. 8C shows the distribution of droplet diameters of 489 dropletsmeasured after emulsification using the ROX fluorescence signal.

FIG. 9 shows frequency distributions of the ratio of green-to-redfluorescence intensities for populations of polydisperse droplets loadedwith three different starting concentrations of dsDNA (i.e., ˜2×10³dsDNA copies/μL in Histogram 10A, ˜2×10⁶ dsDNA copies/4 in Histogram10B, and ˜2×10⁷ dsDNA copies/4 in Histogram 10C). At the lowestconcentration, essentially no droplets contain an amplified DNA samplefollowing PCR (Histogram 10A). This distribution consists mostly ofdroplets lacking amplified products with a mean FAM/ROX ratio of 0.35(N=1701 droplets). At the middle concentration some droplets contain anamplified DNA sample following PCR, whereas others do not (Histogram10B). At this initial target molecule concentrations (˜2×10⁶molecules/μL), two clear distributions are visible (Histogram 10C),corresponding to non-amplified droplets (white bars) similar to thoseshown in Histogram 10A, and amplified droplets (black bars) havingFAM/ROX ratios greater than 0.625. This value is over 1.5 times greaterthan the mean of the non-amplified droplets, making it an appropriatethreshold for distinguishing between droplets that do or do not containamplified sample. At the highest concentration, essentially all dropletscontain an amplified DNA sample following PCR (Histogram 10C). At evenhigher initial target molecule concentrations (˜2×10⁷ molecules/μL),almost all of the emulsion droplets have FAM/ROX ratios above thethreshold for detection of amplified sample (Histogram 10C).

Example 8 Method for Droplet Analysis Following dPCR

This Example describes a digital amplification analysis method usingcontinuous variable droplet volumes, such as digital PCR in apolydisperse droplet emulsion system. Using this method, a target sampleconcentration, C_(S), can be accurately determined using digital assayswith polydisperse droplets.

The sample is distributed into droplets of variable size and thedistribution of target molecules into the droplets follows Poissonstatistics. Although this example provides a method for calculatingsample concentration, it will be understood that other suitable methodscan be used to determine sample concentration. In this example, initialsample concentration (C_(S)) is expressed as a number of molecules in agiven volume. The sample is distributed into discrete partitions or“droplets” of variable volumes, where the distribution of targetmolecules into the droplets follows Poisson statistics. For each dropletin the digital array, and as shown in Equation (5), the average numberof targets depends on its volume, and the initial sample concentration,C_(S):

$\begin{matrix}{{P\left( {n,{C_{S}V_{i}}} \right)} = {\frac{\left( {C_{S}V_{i}} \right)^{n}}{n!}{\exp\left( {{- C_{S}}V_{i}} \right)}}} & (5)\end{matrix}$

P(n,C_(S)V_(i)) is the probability of finding n molecules in a dropletof volume V_(i) for a given concentration C_(S) of target molecules insolution. The amplification reaction will cause a droplet containing oneor more molecules to be distinguishable from empty droplets by means ofa reporter, such as the fluorescence reporter described in Example 7. Inthis method, it is only known whether a droplet is empty (n=0) oroccupied (n>0). The associated probabilities are shown in Equations (6)and (7) below:P(0,C _(S) V _(i))=exp(−C _(S) V _(i))P(n>0,C _(S) V _(i))=1−exp(−C _(S) V _(i))  (6) & (7)

In order to determine the concentration, C_(S), of target molecules,P(n>0, C_(S)V_(i)) can be summed over a large number of droplets withrespective volumes, V_(i).

For each analysis step, a fixed number of droplets, N_(d), is present,and those droplets have a given concentration of target molecules,C_(S). Droplet diameters vary randomly and the size distribution forthose droplets is shown in FIG. 10. This distribution is comparable tothe experimental distribution measured in FIG. 8C. The distribution is alog normal distribution in which only diameters between 8 and 64 micronsare included.

The various droplets have a concentration, C_(S), of target molecules,and in some instances, the concentration, C_(S), can be zero, which isindicative of a lack of target analytes in a given droplet. The totalnumber of droplets determined to contain target analyte, N_(S), iscounted and subsequently compared to the expected number of occupieddroplets, N_(E) as described in Equation (8) below:

$\begin{matrix}{N_{E} = {\sum\limits_{i = 1}^{N_{d}}\left( {1 - {\exp\left( {- {CV}_{i}} \right)}} \right)}} & (8)\end{matrix}$

The most probable value of N_(E) is obtained for C=C_(S). Using thevolumes of the N_(d) droplets, Equation (8) can be fit to N_(S) toobtain a best-fit value of the concentration, with C being the onlyadjustable parameter. A Newton-Rhapson algorithm was used to find thezero of N_(S)−N_(E). The initial value of C is obtained by replacingV_(i) in Equation (8) with the median volume of the distribution andsolving for C. The algorithm then typically takes 5-11 iterations forthe changes in C to fall below one part in 10⁵. The value of C at thatpoint is taken to be the best-fit value of C.

These calculations seek to determine how accurately this procedureestimates a given C_(S), and if two different samples yield differentbest-fit values of C, then attempts to calculate the degree ofconfidence that the samples have different concentrations.

This method includes the measurement of the volume of each droplet andits associated error. Errors in droplet diameter can be approximated bya Gaussian-distributed error, which is applied to any given diametermeasurement. Droplet diameters are used to calculate droplet volumes,and thus the error in the droplet diameters give rise to correspondingerrors in the droplet volumes, {circumflex over (V)}_(i), which aresubstituted into Equation (9) to yield the expected number of occupieddroplets based on measured volumes.

$\begin{matrix}{{\hat{N}}_{E} = {\sum\limits_{i = 1}^{N_{d}}\left( {1 - {\exp\left( {{- C}{\hat{V}}_{i}} \right)}} \right)}} & (9)\end{matrix}$

In this example, droplet diameters are determined by microscopy. Theaccuracy of this method can depend on the numerical aperture (NA) of theobjective lens used as well as other components of the imaging system.For imaging a large number of stationary droplets on a surface, the NAwould likely be less than one and the error in diameter measurements istypically 0.5 to 1.0 microns, independent of the size of the droplet.Two different magnitudes of measurement error are considered and aredenoted as E₁ and E₂. For E₁, the standard deviation of theGaussian-distributed error added to a droplet diameter and is the largerof 1 micron or 8% of that droplet's diameter. The relative error isincluded so that the calculation includes a non-negligible measurementerror for the largest droplets. For E₂, the standard deviation of theGaussian-distributed error added to a droplet diameter is the larger of2 microns or 15% of that droplet's diameter. In both cases there is onelimit placed on the measured diameters. If a particular droplet diameterwith measurement error results in the diameter being less than 0.5microns, then that measurement error is discarded and a new one isgenerated for that droplet. The result is an unbiased measurement error.

C_(S) is the actual, unknown concentration that the procedure isattempting to determine, and {circumflex over (V)}_(i) s are the volumesmeasured by the experimenter. C is varied until {circumflex over(N)}_(E) in Equation (9) equals the measured number of occupied dropletsto obtain the best-fit concentration.

Calculations are performed with C_(S)=4.4×10⁻⁵ molecules/fL and N_(d)ranging from 500 to 10000. The droplet sizes were drawn from thedistribution of diameters shown in FIG. 10, which depicts a clipped lognormal distribution of droplet diameters used to validate methods forperforming digital assays. The calculations are repeated for the case ofno measurement error (“0 error”) in the droplet diameters and E₁ and E₂measurement error. For each number of droplets and amount of error, 1000calculations are performed and the average best-fit concentration andthe standard deviation of the distribution of best-fit concentrationsare calculated.

The ratio of the standard deviation to the average best-fitconcentration is called the “Measurement Variability” and is plotted forthe range of droplet numbers and amount of measurement error in FIG. 11.FIG. 11 shows how measurement variability is affected by sample size(i.e., number of droplets). Data are generated for a digital assayperformed with the sample concentration set to 4.4×10⁻⁵ molecules/fL.Measurement variability reflects the accuracy of a digital assay inestimating the true concentration of a sample, with more measurementvariability implying less accuracy. For this simulation, measurementvariability (vertical axis) is defined as the ratio of the standarddeviation divided by the mean of the estimated concentrationdistribution. Measurement variability is calculated for differentnumbers of droplets (drawn from the droplet diameter distribution shownin FIG. 10), and for three different amounts of error in the simulatedmeasurement of droplet diameters. In one set of calculations, themeasurement of droplet diameters had no errors (“0 error”). In anotherset of calculations, the standard deviation of the droplet diametererror distribution is the larger of 1 μm or 8% of the true dropletdiameter (“E₁ error”). In a third set of calculations, the standarddeviation of the droplet diameter error distribution is the larger of 2μm or 15% of the true droplet diameter (“E₂ error”). The similarity inthe measurement variability for the three different amounts of dropletdiameter measurement errors suggests that the measurement variabilityfor any given sample is dominated by the Poisson statistics, whichgovern the distribution of target molecules among the droplets. As aresult, any variability in the best-fit concentration due todroplet-size measurement errors has a small or negligible impact on theconcentration determination, so long as it is unbiased.

The ability of a method to distinguish a difference in concentrationscan be described in terms of confidence and power. This aspect isdescribed by Lieber, R. L. (1990) “Statistical Significance andStatistical Power in Hypothesis Testing,” J. Orthopaedic Research 8,304-309. The present method enables one to determine the confidencelevel for a given measurement, which is particularly relevant whenmeasurements on two different samples yield two different best-fitconcentrations (C₁ and C₂). Thus, it would be useful to know howconfident one can be in asserting that the concentrations of the twosamples are different, and also the probability of being wrong if oneconcluded that they were not different. The risk of a false positiveresult (Type I error) is controlled by requiring that the results have arequired minimum confidence and the risk of a false negative result(Type II error) is controlled by requiring that the method have arequired power.

For the comparison of two best-fit concentrations from two differentsamples, the null hypothesis would be that the two samples have the same(unknown) concentration. If a is the probability that two samples withthe same concentration can result in best-fit concentrations that differin magnitude by more than |C₁ and C₂|, then (1−α) is the confidenceassociated with rejecting the null hypothesis. The acceptable minimumvalue of (1−α) is chosen to limit false positive results. The use of thepower to guard against false negatives is described below.

One method used to estimate confidence levels is the Z-test as shown inEquation (10):

$\begin{matrix}{Z = \frac{C_{1} - C_{2}}{\sqrt{\sigma_{1}^{2} + \sigma_{2}^{2}}}} & (10)\end{matrix}$

A confidence level of 95% is a common choice and requires Z>1.96. Thevalue of C_(n) is derived from the best-fit results of Equation (9), andan is the variance associated with the measurement of C_(n). In thisexample, σ_(n) ² is estimated because it is believed that there is notractable analytical expression for this term. A second simulationmethod to estimate the confidence is performed and compared with the Zmethod results. Hereafter, the two methods are denoted the Z method andthe Pairs method (or P method).

For the Z method estimate of the confidence, two different values ofC_(S) are used (C_(S1) and C_(S2)). For C_(S1), a set of 5000 dropletsis randomly selected from the clipped log normal distribution andEquation (6) is used to calculate the number of occupied droplets. TheE₁ size of measurement errors is used to generate volumes, {circumflexover (V)}_(i). A best value of the concentration, C₁, is obtained usingEquation (8) as described above. The standard deviation is estimated byperforming N_(Z)=1000 additional calculations. For each, the amount ofvariability due to Poisson statistics is determined by taking the set ofmeasured volumes, {circumflex over (V)}_(i) and using Equation (6) todetermine which of them is occupied. The number occupied are then fitusing Equation (8) to obtain a best-fit concentration for eachadditional calculation. The standard deviation of the additional N_(Z)calculations is used for σ₁ in Equation (9). This process is thenrepeated for C_(S2). An estimate of the confidence can be calculatedfrom the best-fit concentrations, C_(n), and the measured dropletvolumes {circumflex over (V)}_(i) using Equation (9).

For the P method estimate of the confidence, the null hypothesis is thatthe two best-fit results (C₁ and C₂) are each obtained from a samplewhose actual concentration, C, is the average of the two best-fitconcentrations. N_(p)=500 additional sets of droplet diameters aredetermined and for each, the number of occupied droplets are determinedfor the concentration, C, and the E₁ size of measurement errors are usedto generate measured volumes. A best-fit concentration C′ is obtainedfor each set. Then M_(p)=500 pairs of values are randomly selected withreplacements from the set of C′ and the absolute value of theirdifferences (δC′_(p), p=1, . . . , M_(p)) are compared with ΔC=C₂−C₁.The fraction of the δC′_(p) that are greater than ΔC provides anestimate of a, i.e., the probability that two measurements made from asample with concentration C would differ from each other by more thanΔC. The P method estimate of α is used to calculate the confidence,which equals (1−α).

The entire procedure for obtaining two estimates of the confidence isrepeated for pairs of C_(S) values 100 times. For each repetition, a newset of volumes is generated for each C_(S) and Equations (6) and (7) isused to generate the number of occupied droplets for each C_(S).Measured volumes are generated and used in Equation (9) to fit theresults and obtain a new pair of best-fit concentrations (C₁ and C₂).The difference between confidences calculated for a given pair ofmeasurements by the Z method and P methods are typically less than 1%,so either method can be used to calculate the power. One advantage ofthe Z method for analyzing measurements is that it does not require anumerical method for generating distributions of droplets.

The P method can also be used to analyze measurement values. For twodifferent concentrations, the power is the fraction of the results thatexceeds a desired value of the confidence, (1−α). Determinations of thepower in distinguishing two concentrations that differ by 50% areperformed using N_(d)=5000 droplets and E₁ measurement error. Theresults are plotted in FIG. 12 as a function of the smaller of the twoconcentrations. In FIG. 12, the standard deviation of droplet diametermeasurement error is the larger of 1 μm or 8% of the droplet diameter(“E₁ error”). The dashed line marks a power of 0.95, which correspondsto a 5% chance of failing to detect a difference in the two sampleconcentrations (a false negative, or Type II error). The solid line isthe power for distinguishing the case of two concentrations that differby 50% when the confidence level, (1−α), equals 0.95. For a confidencelevel of 95% (which discriminates against false positives or Type 1error) the dynamic range is defined as the ratio of the maximum andminimum concentrations for which the Type 2 error (i.e., falsenegatives) is 5% or less (power >0.95). This point is seen in FIG. 12 atthe ratio of the larger concentration where the solid and dashed linescross divided by the smaller concentration where the solid and dashedlines cross.

FIG. 13 is a graph depicting the relationship between sample size(number of droplets, shown on the horizontal axis) and dynamic range(shown on the vertical axis) of a digital assay when performed onpolydisperse droplets (gray circles, diameters obtained from thedistribution in FIG. 10) with droplet diameter measurement error (“E₁error”) or monodisperse droplets (black triangles, all diameters exactly30 μm) with no droplet diameter measurement error. The dynamic rangedescribes how broad the range of concentrations is for which the assaycan be used effectively. Specifically, the dynamic range is defined asthe ratio of the maximum and minimum concentrations for whichstatistical power is greater than 0.95, assuming a confidence level of95% (5% chance of a false positive, or type I error). The digital assayis effective for a much broader range of concentrations when it isperformed on polydisperse droplets compared with monodisperse droplets.As shown in FIG. 13, for the same number of droplets, the digital assayhas a significantly larger dynamic range when using a distribution ofpolydisperse droplets than can be obtained using a distribution ofmonodisperse droplets. For this reason, the use of polydisperse dropletsis analytically superior to the use of monodisperse droplets.

FIG. 1 is a gray-scale image of an exemplary polydisperse dropletemulsion system obtained using confocal fluorescent microscopy.

FIGS. 5A and 5B depict the results of the initial steps of the ReverseWatershed Method as applied to the image in FIG. 1, including theidentification of regions of interest (ROIs) as shown in FIG. 5A and thefinal, processed image with optimized circular regions as shown in FIG.5B, from which information on droplet size and target molecule presencecan be determined.

FIG. 6A shows a processed image produced after performing the initialsteps of the Circle Detection Method as applied to the image of FIG. 1.FIG. 6B shows the final results obtained after sorting circles in FIG.6A to identify and locate droplets.

Example 9 Characterization of Droplet Diameter Changes

This Example describes the analysis of changes in the distribution ofdroplet sizes in a polydisperse droplet emulsion system under PCRconditions and methods for minimizing the impact of such changes.

Droplet size can change for a number of reasons, including as a resultof evaporation or droplet fusion. Droplets in an emulsion system canexperience significant temperature fluctuations, such as those thatoccur in PCR thermal cycling. Evaporation may occur within the dropletsover the course of thermal cycling, which can alter the distribution ofdroplet diameters and volumes. Further, droplets sitting in proximity toone another may in some instances fuse with each other due to thetendency to reduce the overall surface tension of the droplet-containingsystem. Changes in droplet diameter and volume over the course of adigital assay can lead to measurement error if the change issignificant. This Example sets forth steps to characterize and optimizethe measurement system and ensure the accuracy of the size distributionmeasurements, including investigating the effects of heating andmechanical manipulation on droplet sizes.

Droplet Fusion.

Two emulsions were prepared using a mixture of general PCR reagents. Thefirst emulsion excluded both a DNA template and a green fluorescentprobe (FAM), while the other emulsion excluded both a DNA template and ared fluorescent dye (ROX). In the latter, the final concentration of thegreen fluorescent probe (FAM) was increased to 1.4 μM. The two emulsionswere allowed to settle and stabilize for 10 min. Then they were gentlyre-suspended and combined with slow tilting motions of the tube. Lastly,the combined mixture was aliquoted into three PCR tubes. The first tubewas set off to the side as a no-heating (control) sample. The remainingtwo were thermal cycled under standard conditions the following cyclingdurations (including a hot start): 1 or 50 cycles. A replicate set wasrun concurrently.

FIG. 14 shows the frequency of droplet fusion events that occurredeither spontaneously, or as a result of thermal cycling, in polydispersedroplet emulsions. The ROX and FAM fluorescence intensities of theemulsion mixture were used to identify fusion events. The frequency ofdroplet fusion events is reflected in the percent of droplets containingboth ROX and green fluorescent probe. Droplets denoted with a circlecontained both dyes (Image 14A and Image 14B). FAM and ROX fusion eventssolely due to post-emulsification droplet instability, sample handling,and pipetting were shown to be minimal, i.e., at a rate of 6.2±2.1%(Chart 14C). It should be noted that this measurement does not includefusion events between droplets containing the same dye, but it would beexpected to be comparable in value. After a hot start and one thermalcycle, heating applied to the emulsion sample resulted in comparablefusion events of 6.1±1.4% (Chart 14C). The FAM-ROX fusion eventsdetected for 50 cycles, 5.8±1.5%, was also similar to that of one cycle(Chart 14C). Both heating conditions were well within the range of errorof the control aliquot.

It is important to note that fusion events did not appear toprogressively increase with respect to thermal cycling duration. Thissuggests that thermal cycle heating induced little to no droplet fusion,and the main factors contributing to droplet instability were related tothe mixing of the two color emulsions and sample handling. This issignificant because fusion events that occur before or early duringthermal cycling will not skew the results of the assay, since mergeddroplets that contain at least one target molecule will undergoamplification and give a positive signal, whereas merged droplets thatdo not undergo amplification will give a negative signal. In contrast,fusion events occurring later during thermal cycling can result in amerged droplet falling below the binary detection threshold of an assay,resulting in the droplet being incorrectly characterized. The results ofthe experiment indicate that fusion should have a minimal effect onsample quantification using this method. Additionally, if samplehandling were to be entirely eliminated from the process by performingemulsification and thermal cycling all on the same device, fusion canhave even less of an impact on the results of the assay. An example of apotential workflow eliminating sample handling post-emulsification isshown in FIG. 4.

Droplet Shrinkage.

Analysis of droplet shrinkage was carried out by comparing the dropletsize distribution of a negative control and thermal cycled emulsionsample. Emulsions were prepared using the standard PCR mix andemulsification process. The same thermal conditions as the fusionexperiments were examined. The droplet diameter distribution of theemulsion samples were normalized and plotted in FIG. 15, which comparesthe distribution of droplet diameters in polydisperse droplet emulsionssubjected to either no heating, 1, or 50 thermal cycles. This experimentwas conducted to quantify changes in droplet size resulting fromrepetitive thermal cycling. The control set had a mean diameter of15.4±0.1 μm (1857 droplets measured). Polydisperse droplet emulsionssubjected to one thermal cycle (triangles in FIG. 15) had a meandiameter of 14.9±0.4 μm (1952 droplets measured). Polydisperse dropletemulsions subjected to 50 thermal cycles (circles in FIG. 14) had a meandiameter of 15.8±0.5 μm (1660 droplets measured). The distributions ofdroplet diameters for the three conditions were indistinguishable,indicating that thermal cycling does not result in appreciable changesin droplet volume.

Example 10 Comparison Between Best-Fit Concentrations and ConcentrationsDetermined by UV Absorbance

This Example describes the good agreement observed between sampleconcentrations determined by best-fit methods of the present disclosureand those measured by UV absorbance.

The best-fit concentrations of serial dilutions of erbB2 dsDNA werecompared with concentrations determined by absorbance measurements at260 nm. The concentrations spanned a range of four orders of magnitude(i.e., 2×10³, 2×10⁴, 2×10⁵, and 2×10⁶ dsDNA copies/μL) with multiplesamples at each concentration. The droplet diameters were determinedusing the Simple Boundary Method as described herein and the analysisincluded droplets with diameters ranging from 7 to 50 μm (1 to 500 pLvolumes). Additional PCR parameters were consistent with those describedin EXAMPLE 7. The best-fit concentrations were obtained using Equation(8) below:

$\begin{matrix}{N_{E} = {\sum\limits_{i = 1}^{N_{d}}\left( {1 - {\exp\left( {- {CV}_{i}} \right)}} \right)}} & (8)\end{matrix}$

FIG. 18. is a graph depicting the relationship between sampleconcentration values as determined by a best-fit method (shown on thevertical axis) and as determined by absorption measurements at 260 nm(shown on horizontal axis) for the erbB2 dsDNA samples described above.The comparison in FIG. 18 shows the good agreement between the twomethods as indicated by the linear relationship between them.

Example 11 Droplet Analysis Using the Most Probable Number Method

This Example describes the use of the Most Probable Number (MPN) Methodfor determining the concentration of a target sample (by contrast tousing Equation (8) as described in EXAMPLE 8). Using this method, theconcentration, C_(S), of a target sample is accurately determinedwithout identifying, sizing or enumerating unoccupied droplets.

For the specific case involving chambers and wells, the number ofchambers or wells containing the target sample was first determined. Thenumber of chambers was predetermined before the assay was performed. Thevolume of each chamber was one of a discrete set of sizes, which werealso predetermined before performing the assay.

For the specific case involving chambers and wells, the MPN equivalentof Equation (8) is shown below as Equation (11):

$\begin{matrix}{{\sum\limits_{i = 1}^{m}{n_{i}V_{i}}} = {\sum\limits_{i = 1}^{m}\frac{\left( {n_{i} - b_{i}} \right)V_{i}}{\left( {1 - {\exp\left( {{- V_{i}}C} \right)}} \right)}}} & (11)\end{matrix}$In Equation (11), there are m different sizes of chambers. For the ithsize, the volume of each chamber was V_(i) and there were n_(i) chambersof that size. After the reaction was run, b_(i) is the number ofchambers of the ith size that were unoccupied. The equation was then fitto obtain C, the concentration of the solution.

In this method involving droplets, the left-hand term in Equation (11)is the total volume of all the droplets. The droplets all have differentsizes so each of the n_(i) is equal to one and the sum of all the n_(i)equals the total number of droplets. There were m different sizes, and asummation was performed for all droplets. Because b_(i) is one for anunoccupied droplet and zero for an occupied droplet, the (n_(i)−b_(i))term causes the sum on the right-hand side of Equation (11) to be a sumover only occupied droplets, and thus Equation (11) can be simplifiedand represented as Equation (12) below:

$\begin{matrix}{V_{total} = {\sum\limits_{i = 1}^{m}\frac{O_{i}V_{i}}{\left( {1 - {\exp\left( {{- V_{i}}C} \right)}} \right)}}} & (12)\end{matrix}$where O_(i) is one for occupied droplets and zero otherwise. Thisequation can also be solved iteratively for C. Simulations performedusing Equation (12) and Equation (8) yield nearly identical results withthe differences being less that the statistical errors in the fit.

As mentioned above, the terms in the sum of Equation (12) are zero forunoccupied droplets. Thus, if the total volume of the sample is known,then it is possible to identify and determine the size of the occupieddroplets in the sample, after which Equation (12) can be used todetermine sample concentration. According to this method, there is noneed to identify the presence or size of unoccupied droplets.

Two different fluorescent dyes are used in methods that require sizingboth occupied and unoccupied droplets. For example, Dye 1, which isfluorescent in all droplets, is used to size the droplets and Dye 2,which only fluoresces significantly in occupied droplets, is used todetermine if the droplet is occupied. However, in a further aspect ofthe Example, using Equation (12) it is possible to execute the methoddescribed in this Example using only Dye 2. Thus, the fluorescence ofDye 2 is used to identify both the presence and size of occupieddroplets.

When the concentration is small, the number of occupied droplets iscorrespondingly small. In that case, a significant volume of emulsion isscanned for the modest number of occupied droplets. Because this methodrequires only that occupied droplets need to be sized, there aresignificantly fewer droplets requiring analysis, which in turnsignificantly reduces the analysis time of the method. In addition, atlow concentrations, it is unlikely that two occupied droplets wouldtouch each other. Because few analyzed droplets are touching, fewercalculations distinguishing those droplets are required. Thus, thecomputational requirements are significantly reduced using this method,thereby simplifying the process of scanning larger sample volumes fordroplets. The ability to more easily scan larger volumes simplifies theanalysis of low concentration samples, thereby increasing the method'ssensitivity.

The Most Probable Number (MPN) Method described in this Example can becombined with the other methods described herein, with the modificationthat when using the MPN Method, there is no need to analyze the imagesof the unoccupied droplets. Any of the image processing algorithmsdescribed in the present disclosure can be used in combination with theMPN Method of this Example, for instance, by setting the threshold pixelintensity to exclude droplets lacking the target sample and analyzingonly those containing the target sample.

Example 12 Index Matching to Improve Imaging Depth

In this Example, the benefits of matching the refractive indices of twoor more immiscible fluids for purposes of optical imaging an emulsionsystem are described.

The ability to match the refractive index of the fluids that make up thediscrete phase and continuous phase can enhance the data acquisitioncapabilities. When the refractive indices do not match, the illumination(or imaging) path can be deflected or distorted, leading to a loss ofsignal during data acquisition. The curved surfaces of the emulsiondroplets become microlenses that diffract and scatter illumination, andimaging deeper into the solution increased the severity of aberrationsin acquired data. In effect, the droplet boundaries became lessdiscernible from the increasing number of overlapped droplets theillumination source must travel through as the plane of view is focuseddeeper (Z dimension) into the sample (FIG. 16, A1-A5).

FIG. 16 shows the improvements in data acquisition capabilities thatwere achieved with refractive index matching of the fluids making up apolydisperse droplet emulsion. Fluorescence images were acquired atprogressively deeper (from left to right) focal planes from twodifferent emulsions (depicted in FIG. 16, A1-A5 and FIG. 16, B1-B5,respectively) with a confocal microscope. Both emulsions were made using73% Tegosoft DEC, 20% light mineral oil, and 7% Abil WE09 oil mix(refractive index 1.4) as the continuous carrier phase. For FIG. 16,A1-A5, the droplets were composed of PCR reagents dissolved in aqueoussolution (refractive index=1.33). For FIG. 16, B1-B5, the droplets werecomposed of PCR reagents dissolved in a water (50% by weight) andglycerol (50% by weight) mixture (refractive index=1.398). In theaqueous sample (FIG. 16, A1-A5), the refractive indices of the twoimmiscible fluid components are disparate, and the droplet boundariesbecome progressively less clear in images acquired at deeper planes offocus, as in FIG. 16, A5. In one aspect the significantly higherrefractive index of the oil mixture (n 1.4) compared to water (n=1.33)led to a series of index matching tests involving the addition of highindex components, such as glycerol (100% (w/w), n=1.474) and sucrose(65% (w/w), n=1.4532), to the PCR mix. In the mixed water and glycerolsample (FIG. 16, B1-B5), the refractive indices of the two immisciblefluid components are similar, and the droplet boundaries remain cleareven in images acquired at deeper planes of focus, as in FIG. 16, B5.

Fluorocarbon oil emulsion systems were also investigated in an attemptto better match their refractive indices. While mineral oil systems havea refractive index significantly higher than water, fluorocarbon systemstypically have a refractive index slightly lower than water (e.g.,perfluorodecalin, Fluorinert FC-40, Fluorinert FC-70, Krytox,—see Table1 above). Perfluorinated compounds that contain aromatic groupstypically have refractive indices higher than water, so in this systemthe composition of the oil can be altered to improve the index matching.An oil phase containing 45% (v/v) Fluorinert FC-40 with 5% Pico-Surf 1and 55% (v/v) octafluorotoluene mixed with PCR aqueous phase wasinvestigated. The mixture was vortexed at 3000 rpm for 30 s. Due to thelower density of the water compared to the fluorocarbon oil phase (seeTable 1), the w/o droplets floated above the oil phase. While thisrequired removal of excess oil to image the w/o droplets within theworking distance of the microscope, this combination improved the imagequality of z-sections acquired deeper in the sample. The boundarydistortions of droplets was much reduced and allowed for a greater rangein building the 3D profile of droplet dimensions.

Attempts were made to minimize changes in the boiling point of anyoil-phase components, which should remain inert at temperatures of 95°C. Effort was also made to reduce or eliminate any impact of emulsionsystem additives on the sample or PCR reagents.

Example 13 Multiple Emulsions to Control Density and Spacing

This Example describes the benefits of using multiple emulsions for adigital assay.

When there is a mismatch in refractive index between emulsion systemcomponents, it can be desirable to position the droplets as close aspossible to the microscope objective during imaging. For an invertedmicroscope, it is possible to allow the droplets to settle on the bottomof the container, assuming the droplet density is greater than thedensity of the surrounding fluid. When mineral oil is used as acontinuous carrier phase, the aqueous droplets are denser than thecontinuous phase, which causes them to settle on the bottom. However,when fluorocarbon-based oils are used as a continuous carrier phase,aqueous droplets will float to the top of the fluid.

The location of the sample droplets can be controlled through the use ofdouble emulsions. In a water/oil/water double emulsion system, afluorocarbon oil can be used as a middle layer, which causes aqueousdroplets to sink to the bottom of the outer aqueous phase.

Two surfactants were tested (e.g., Tween 20 and Span 80) for theproduction of a secondary water layer. A system including 1% Span 80 wasfound to effectively yield a secondary water layer. It was observed thatwater/oil/water emulsions formed with pure fluorocarbon oil (e.g.,FC-40) or in some combination with fluorocarbon solvents for indexmatching had large amounts of water/oil droplets clumped in thesecondary droplet. Highly viscous fluorocarbon oils such as KrytoxGPL-107 were added to increase the viscosity of F_(C)-40 such that thewater/oil emulsion does not immediately rise and clump together abovethe bulk oil phase. With this method, generated water/oil/wateremulsions were less likely to have large amounts of water/oil dropletsclumped inside the secondary droplet (FIG. 17). Spacing of aqueousdroplets can be controlled by varying the viscosity of the oil phase.

FIG. 17 shows fluorescence images of a water/oil/water double emulsionmade in a two-step emulsification process: First an aqueous solutioncontaining PCR reagents was emulsified in an oil mixture composed ofKrytox GPL-107, Fluorinert FC-40 and Pico-Surf 1 surfactant. Theresulting water/oil emulsion was then further emulsified into an aqueoussolution composed of water and Span 80 surfactant to produce awater/oil/water double emulsion. Because the oil phase is, in this case,denser than either aqueous phase, gravity lowers the double-emulseddroplets into closer proximity to the imaging objective. Images wereacquired with a confocal microscope at progressively deeper (from leftto right) focal planes (in 3 μm intervals). In addition to providing theadvantage of better separating droplets, which can result in improvedimaging, these results demonstrate that double emulsions can be helpfulin minimizing the impact of refractive index mismatching by modifyingthe density of the droplets.

While preferred aspects of the present invention have been shown anddescribed herein, it will be obvious to those skilled in the art thatsuch aspects are provided by way of example only. Numerous variations,changes, and substitutions will now occur to those skilled in the artwithout departing from the invention. It should be understood thatvarious alternatives to the aspects of the invention described hereincan be employed in practicing the invention. It is intended that thefollowing claims define the scope of the invention and that methods andstructures within the scope of these claims and their equivalents becovered thereby.

What is claimed is:
 1. A method for performing a digital assay,comprising: measuring a largest diameter of a droplet of a plurality ofpolydisperse droplets, wherein at least some droplets of the pluralityof polydisperse droplets comprise a sample comprising a molecule ofinterest; amplifying the sample to produce an amplified product;associating the amplified product with a detectable agent; determining avolume of the droplet from the largest diameter of the droplet;optically detecting the presence or absence of the sample in theplurality of polydisperse droplets, wherein optically detecting thepresence or absence of the sample in the plurality of polydispersedroplets comprises optically detecting the presence or absence of thedetectable agent in the plurality of polydisperse droplets; anddetermining a concentration of the molecule of interest in the pluralityof polydisperse droplets based on the presence or absence of the samplein the plurality of polydisperse droplets and the volume of the droplet.2. The method of claim 1, wherein measuring the largest diameter of thedroplet comprises: fitting a curve to a circle diameter of the droplet;and interpolating the largest diameter from the curve.
 3. The method ofclaim 1, wherein measuring the largest diameter of the droplet comprisesmeasuring a boundary of the droplet.
 4. The method of claim 1, furthercomprising obtaining an image of the droplet.
 5. The method of claim 1,further comprising obtaining an image stack for the droplet.
 6. Themethod of claim 5, wherein the image stack comprises a plurality ofimages taken from separate depths of focus through the droplet.
 7. Themethod of claim 5, wherein measuring the diameter of the dropletcomprises: correlating the droplet between a plurality of images of theimage stack; and measuring the largest diameter of the droplet in theplurality of images.
 8. The method of claim 1, wherein the molecule ofinterest is selected from the group consisting of a nucleic acidmolecule, a peptide, a protein, and a lipid.
 9. The method of claim 1,wherein amplifying the sample comprises performing polymerase chainreaction (PCR), rolling circle amplification (RCA), nucleic acidsequence based amplification (NASB A), loop-mediated amplification(LAMP), strand displacement amplification, helicase-dependentamplification, circular helicase-dependent amplification, transcriptionmediated amplification (TMA), self-sustained sequence replication (3SR),and single primer isothermal amplification (SPIA), signal mediatedamplification of RNA technology (SMART), branched rolling circleamplification (HRCA), exponential amplification reaction (EXPAR), smartamplification (SmartAmp), isothermal and chimeric primer-initiatedamplification of nucleic acids (ICANS), and multiple displacementamplification (MDA), isothermal multiple displacement amplification, ora combination thereof.
 10. The method of claim 1, wherein amplifying thesample comprises performing antibody-based amplification.
 11. The methodof claim 1, wherein amplifying the sample comprises performing digitalELISA.
 12. The method of claim 1, wherein optically detecting theconcentration of the sample in the plurality of polydisperse dropletsincludes optically detecting the concentration of the molecule ofinterest based on a number of droplets in the plurality of polydispersedroplets with one or more molecules of interest.
 13. The method of anyone of claim 1, wherein a distribution of droplet diameters comprises astandard deviation greater than 100%, greater than 50%, greater than30%, greater than 20%, greater than 15%, greater than 10%, greater than9%, greater than 8%, greater than 7%, greater than 6%, or greater than5% of the median droplet diameter.
 14. The method of any one of claim 1,wherein a distribution of droplet diameters comprises a standarddeviation greater than 100%, greater than 50%, greater than 30%, greaterthan 20%, greater than 15%, greater than 10%, greater than 9%, greaterthan 8%, greater than 7%, greater than 6%, or greater than 5% of themean droplet diameter.
 15. The method of any one of claim 1, whereinvolumes vary by more than a factor of about 2, more than a factor ofabout 10, or by more than a factor of about
 100. 16. The method of anyone of claim 1, further comprising producing the plurality ofpolydisperse droplets.